Projeto Ótimo de Malhas hp Adaptativas

Abstract: An optimum hp adaptive mesh desigh is accomplished by minimizing the number of equations for a specified error limit.  This new approach leads to a problem in which the h and p mesh parameters appear explicitly in the formulation.  The optimal conditions yields to a very simple non-linear one-variable equation for each element which simultaneously supplies the optimum values for the h and p parameters.  The methodoloty here developed is applied in the numerical solution of several 1D and 2D elliptic boundary value problems, where the solution is specially constructed in order to produce great local variations due to singularities or high gradients. In all cases, a very fast convergence rate is achieved within only a few iterations steps.