Validation of Recipes for the Recovery of Stresses and Derivatives by a Computer-Based Approach

摘要

In this paper we present a methodology for checking the local quality of recipesfor the recovery of stresses or derivatives from finite element solutions of linear elliptic problems. The methodology accounts precisely for the factors which affect the local quality of the recovered quantities, namely, the geometry of the grid, the polynomial degree and the type of the elements, the coefficients of the differential equation and the class of solutions of interest. We give examples of how the methodology can be used to obtain precise conclusions about the quality of a class of recipes, based on least-squares patch-recovery, in the interior of complex grids, like the ones employed in engineering computations. By using this approach we were able to discover recipes which are much more robust than the ones which are currently in use in the various finite element codes.