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Generalizing the Multiscale Hybrid-Mixed Method for Reactive-Advective- Diffusive Equations
Computer Methods in Applied Mechanics and Engineering, Vol. 428, pp. 117089, 2024
Abstract
In this work, we propose a new method called Petrov–Galerkin multiscale hybrid-mixed (PGMHM for short) as a variant of the multiscale hybrid-mixed (MHM) method. Its con- struction starts from a Petrov–Galerkin formulation for the Lagrange multiplier space, defined by enriching the trial spaces with residual-based functions on the partition faces. As a result, jump terms are added to the original MHM method, which penalizes the lack of conformity of MHM numerical solutions. As a consequence of space enrichment, the method induces local post-processing of the numerical solution that incorporates the model’s physical aspects and preserves the exact solution’s local conservation properties. Numerical experiments validate the theoretical results and verify the accuracy of PGMHM on highly heterogeneous problems.
Revisiting the Robustness of the Multiscale Hybrid-Mixed Method: The Face-Based Strategy
Journal of Computational and Applied Mathematics, Volume 436, Pages 115415, 2024
Abstract
In this work, we propose a new method called Petrov–Galerkin multiscale hybrid-mixed (PGMHM for short) as a variant of the multiscale hybrid-mixed (MHM) method. Its con- struction starts from a Petrov–Galerkin formulation for the Lagrange multiplier space, defined by enriching the trial spaces with residual-based functions on the partition faces. As a result, jump terms are added to the original MHM method, which penalizes the lack of conformity of MHM numerical solutions. As a consequence of space enrichment, the method induces local post-processing of the numerical solution that incorporates the model’s physical aspects and preserves the exact solution’s local conservation properties. Numerical experiments validate the theoretical results and verify the accuracy of PGMHM on highly heterogeneous problems.
A Petrov-Galerkin Multiscale Hybrid-Mixed Method for the Darcy Equation on Polytopes
Computational and Applied Mathematics, Volume 42, Number 173, 2023
Abstract
In this work, we propose a new method called Petrov–Galerkin multiscale hybrid-mixed (PGMHM for short) as a variant of the multiscale hybrid-mixed (MHM) method. Its con- struction starts from a Petrov–Galerkin formulation for the Lagrange multiplier space, defined by enriching the trial spaces with residual-based functions on the partition faces. As a result, jump terms are added to the original MHM method, which penalizes the lack of conformity of MHM numerical solutions. As a consequence of space enrichment, the method induces local post-processing of the numerical solution that incorporates the model’s physical aspects and preserves the exact solution’s local conservation properties. Numerical experiments validate the theoretical results and verify the accuracy of PGMHM on highly heterogeneous problems.
The MHM Method for Elasticity on Polytopal Meshes
IMA Journal of Numerical Analysis, Volume 43, Number 3, Pages 2265–2298, 2023
Abstract
The multiscale hybrid-mixed (MHM) method consists of a multi-level strategy to approximate the solution of boundary value problems with heterogeneous coefficients. In this context, we propose a new family of finite elements for the linear elasticity equation defined on coarse polytopal partitions of the domain. The finite elements rely on face degrees of freedom associated with multiscale bases obtained from local Neumann problems with piecewise polynomial interpolations on faces. We establish sufficient conditions on the fine-scale interpolations such that the MHM method is well-posed and optimally convergent under local regularity conditions. Also, a multi-level error analysis demonstrates that the MHM method achieves convergence without refining the coarse partition. The upshot is that the Poincar\'e and Korn's inequalities do not degenerate, and then the convergence arises on general meshes. Two- and three-dimensional numerical tests assess theoretical results and verify the robustness of the method on a multi-layer media case. Also, we address the computational aspects of the underlying parallel algorithm, which highlight the best compromise between execution time and memory allocation for a given error threshold.
Bridging the Multiscale Hybrid-Mixed and Multiscale Hybrid High-Order Methods
ESAIM: M2AN, Volume 56, Number 1, Pages 261-285, 2022
Abstract
We establish the equivalence between the Multiscale Hybrid-Mixed (MHM) and the Multiscale Hybrid High-Order (MsHHO) methods for a variable diffusion problem with piecewise polynomial source terms. Under the idealized assumption that the local problems defining the multiscale basis functions are exactly solved, we prove that the equivalence holds for general polytopal (coarse) meshes and arbitrary approximation orders. Also, we leverage the interchange of properties to perform a unified convergence analysis, as well as to improve on both methods.
An Adaptive Multiscale Hybrid-Mixed Method for the Oseen Equations
Advances in Computational Mathematics, Volume 47, Number 15, Pages 1-15, 2021
Abstract
A novel residual a posteriori error estimator for the Oseen equations achieves efficiency and reliability by including multi-level contributions in its construction. Originates from the Multiscale Hybrid Mixed (MHM), the estimator combines residuals from the skeleton of the first-level partition of the domain, along with the contributions from element-wise approximations. Those second-level contributions infer the accuracy of multiscale basis computations as part of the MHM framework. Also, the face-degree of freedom of the MHM method shapes the estimator and induces a new face-adaptive procedure on the mesh’s skeleton only. As a result, the approach avoids re-meshing the first-level partition, which makes the adaptive process affordable and straightforward on complex geometries. Several numerical tests assess theoretical results.
New H(div)-Conforming Multiscale Hybrid-Mixed Methods for the Elasticity Problem on Polygonal Meshes
ESAIM: Mathematical Modelling and Numerical Analysis, Volume 55, Pages 1005-1037, 2021
Abstract
This work proposes a family of multiscale hybrid-mixed methods for the two-dimensional linear elasticity problem on general polygonal meshes. The new methods approximate displacement, stress, and rotation variables using two-scale discretizations. The first scale level setting consists of approximating the traction variable (Lagrange multiplier) in discontinuous polynomial spaces, and of computing rigid-body modes element wisely. In the second scale level, the methods are made effective by solving completely independent local Newmann elasticity problems written in a mixed form with weak symmetry enforced via a rotation multiplier. Since the finite-dimensional space for the traction variable constrains the discrete space for the local stress tensor, the discrete stress field lies in the H(div) space globally and stays in local equilibrium with external forces. We propose different choices to approximate local problems based on locally stable pairs of finite elements defined on affine second-level meshes. Those choices generate the family of multiscale finite element methods for which stability and convergence are proved in a unified framework. Notably, we prove that the methods are optimal and high-order convergent in the natural norms. Also, it emerges that the approximate displacement and stress divergence are super-convergent in the L2-norm. Numerical verification assess theoretical results and highlight the high precision of the new methods on coarse meshes for multilayered heterogeneous material problems.
A Multiscale Hybrid-Mixed Method for the Helmholtz Equation in Heterogeneous Media
SIAM Journal on Numerical Analysis, Volume 58, Number 2, Pages 1029-1067, 2020
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
The Multiscale Hybrid Mixed Method in General Polygonal Meshes
Numeriche Mathematik, Volume 145, Pages 197-237, 2020
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
On a Multiscale a Posteriori Error Estimator for the Stokes and Brinkman Equations
IMA Journal of Numerical Analysis, Volume 41, Pages 344-380, 2019
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
A Multiscale Hybrid Method for Darcy’s Problems using Mixed Finite Element Local Solvers
Comp. Meth. Appl. Mech. Eng., Volume 354, Pages 213-244, 2019
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
The Multiscale Hybrid-Mixed Method for the Maxwell Equations in Heterogeneous Media
SIAM Multiscale Model. Simul., Volume 16, Number 4, Pages 1648–1683, 2018
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
Multiscale Hybrid-Mixed Method for the Stokes and Brinkman Equations – The Method
Comp. Meth. Appl. Mech. Eng., Volume 324, Pages 29–534, 2017
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
On the Robustness of Multiscale Hybrid-Mixed Methods
Math. Comp., Volume 86, Number 304, Pages 525–548, 2017
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
A Hybrid-Mixed Method for Elasticity
ESAIM: Math. Model. Num. Anal., Volume 50, Number 2, Pages 311–336, 2016
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
On a Multiscale Hybrid-Mixed Method for Advective-Reactive Dominated Problems with Heterogenous Coefficients
SIAM Multiscale Model. and Simul., Volume 13, Number 2, Pages 491–518, 2015
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
A Low-Order Local Projection Method for the Incompressible Navier–Stokes Equations in Two- and Three-Dimensions
IMA Journal of Numerical Analysis, Volume 36, Number 1, Pages 267– 295, 2015
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
An Adaptive Residual Local Projection Finite Element Method for the Navier-Stokes Equations
Advances in Computational Mathematics, Volume 40, Number 5-6, Pages 1093–1119, 2014
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
Multiscale Hybrid-Mixed Method
SIAM J. Numer. Anal., Volume 51, Number 6, Pages 3505–3531, 2013
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
A Family of Multiscale Hybrid-Mixed Finite Element Methods for the Darcy Equation with Rough Coefficients
J. Comput. Phys., Volume 245, Pages 107–130, 2013
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
Numerical Multiscale Methods for a Reaction Dominated Model
Comput. Methods Appl. Mech. Engrg., Volume 201-203, Pages 228–244, 2012
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
Numerical Multiscale Methods
International Journal for Numerical Methods in Fluids, Volume 70, Number 4, Pages 403–419, 2012
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
Convergence Analysis of a Residual Local Projection Finite Element Method for the Navier-Stokes Equations
SIAM J. Numer. Anal., Volume 50, Number 2, Pages 669–699, 2012
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
Supporting the Perpetuation and Reproducibility of Numerical Method publications
Procedia CS, Volume 4, Pages 688–696, 2011
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
Simulating Transient Phenomena via Residual Free Bubbles
Comput. Methods Appl. Mech. Engrg., Volume 200, Number 25-28, Pages 2127–2130, 2011
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
Beyond Pressure Stabilization: A Low Order Local Projection Method for the Oseen Equation
Int. J. Numer. Methods Eng., Volume 86, Number 7, Pages 801–815, 2011
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
A Two-Level Enriched Finite Element Method for a Mixed Problem
Math. Comp., Volume 80, Pages 11–41, 2011
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
A Hierarchical Estimator Combined with a Stabilized Finite Element Method
Numerical Methods for PDE, Volume 28, Number 3, Pages 782–806, 2011
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
Consistent Local Projection Stabilized Finite Element Methods
SIAM J. Numer. Anal., Volume 48, Number 5, Pages 1801–1825, 2010
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
A Residual Local Projection Method for the Oseen Equation
Comput. Methods Appl. Mech. Engrg., Volume 199, Number 27-32, Pages 1906–1921, 2010
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
Stabilization Arising from PGEM: A Review and Further Developments
Appl. Numer. Math., Volume 59, Number 9, Pages 2065–2081, 2009
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
On a Residual Local Projection Method for the Darcy Equation
C. R. Acad. Sci. Paris, Volume 347, Pages 1105–1110, 2009
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
A Symmetric Nodal Conservative Finite Element Method for the Darcy Equation
SIAM J. Numer. Anal., Volume 47, Number 5, Pages 3652–3677, 2009
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
Weighted Quadrature Rules for Finite Element Methods
J. Comput. Appl. Math., Volume 227, Number 1, Pages 93–101, 2008
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
Asymptotics of the Poisson problem in Domains with Curved Rough Boundaries
SIAM Mathematical Analysis, Volume 38, Number 5, Pages 1450–1473, 2007
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
A Stabilized Finite Element Method for the Stokes Problem Including Element and Edge Residuals
IMA Journal of Numerical Analysis, Volume 27, Pages 172–197, 2007
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
A Petrov-Galerkin Enriched Method: A Mass Conservative Finite Element Method for the Darcy Equation
Comput. Methods Appl. Mech. Engrg., Volume 196, Number 2, Pages 2449–2464, 2007
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
Stabilized finite element methods based on multiscale enrichment for the Stokes problem
SIAM J. Numer. Anal., Volume 44, Number 1, Pages 322-348, 2006
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
Enriched finite element methods for unsteady reaction-diffusion problems
Communications in Numerical Methods in Engineering, Volume 22, Number 6, Pages 619-625, 2006
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
Towards Multiscale Functions: Enriching Finite Element Spaces with Local but not Bubble–Like Functions
Comput. Methods Appl. Mech. Engrg., Volume 194, Pages 3006–3021, 2005
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
Relationship between Multiscale Enrichment and Stabilized Finite Element Methods for the Generalized Stokes Problem
C.R. Acad. Sci.Paris, Ser. I, Volume 341, Pages 635–640, 2005
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
Multiscale and Residual–Free Bubble Functions for Reaction–Advection–Diffusion Problems
International Journal for Multiscale Enginnering, Volume 3, Number 3, Pages 297–312, 2005
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
Convergence analysis of a multiscale finite element method for singularly perturbed problems
SIAM Multiscale Model. and Simul., Volume 4, Number 3, Pages 839–866, 2005
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
New wall laws for the Unsteady Incompressible Navier- Stokes Equations
ESAIM: M2AN, Volume 36, Number 2, Pages 177–203, 2002
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
Analysis of Curvature Influence on Effective Boundary Conditions
C.R. Acad. Sci.Paris, Ser. I, Volume 335, Pages 499–504, 2002
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
An Unusual Stabilized Finite Element Method for a Generalized Stokes Problem
Numer. Math., Volume 92, Number 4, Pages 653–677, 2002
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
On an Improved Unusual Stabilized Finite Element Method for the Advective–Reactive–Diffusive Equation
Comput. Methods Appl. Mech. Engrg., Volume 190, Number 13-14, Pages 1785–1800, 2000
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
Rough Boundaries and Wall Laws
International J. Numer. Methods in Fluids, Volume 27, Number 1-4, Pages 169–177, 1998
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
Effective Boundary Conditions for Laminar Flows over Periodic Rough Boundaries
Journal of Computational Physics, Volume 147, Number 1, Pages 187–218, 1998
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
Constructing Wall Laws with Domain Decomposition or Asymptotic Expansion techniques
Comput. Methods in Applied Mechanics and Engineering, Volume 151, Pages 215–232, 1998
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
Domain Decomposition and Wall Laws
Surikasekikenkyusho Kokyuroku, Volume 989, Pages 42–55, 1997
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
Combining Stabilized Finite Element Methods
Comput Appl. Math., Volume 14, Number 3, Pages 285– 300, 1995
Abstract
Although a substantial amount of research has examined the constructs of warmth and competence, far less has examined how these constructs develop and what benefits may accrue when warmth and competence are cultivated. Yet there are positive consequences, both emotional and behavioral, that are likely to occur when brands hold perceptions of both. In this paper, we shed light on when and how warmth and competence are jointly promoted in brands, and why these reputations matter.
Foundations of the MHM method
In G. R. Barrenechea, F. Brezzi, A. Cangiani, and E. H. Georgoulis, editors, Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations, Lecture Notes in Computational Science and Engineering. Springer, 2016.
Proven strategies for harnessing the power of social media to drive social change
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Shape Control versus Boundary Control
In F. Murat et al, Equations aux dérivées partielles et applications. Articles dédiés à J.L.Lions, pages 1-18. Elsevier, 1998
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