Polynomial preserving recovery for meshes from Delaunay triangulation or with high aspect ratio

摘要

A newly developed polynomial preserving gradient recovery technique is further studied. The results are twofold. First, error bounds for the recovered gradient are established on the Delaunay type mesh when the major part of the triangulation is made of near parallelogram triangle pairs with epsilon-perturbation. It is found that the recovered gradient improves the leading term of the error by a factor epsilon. Secondly, the analysis is performed for a highly anisotropic mesh where the aspect ratio of element sides is unbounded. When the mesh is adapted to the solution that has significant changes in one direction but very little, if any, in another direction, the recovered gradient can be superconvergent. (C) 2007 Wiley Periodicals, Inc.