Asymptotically Exact A Posteriori Error Estimators, Part II: General Unstructured Grids

• DOI: 10.1137/s0036142901398751
• Publication Date: 2003-12-23T02:00:49Z
• Authors: Randolph E. Bank; Jinchao Xu
• Keywords: Superconvergence; Hessian matrix; Smoothing

In Part I of this work [SIAM J. Numer. Anal., 41 (2003), pp. 2294--2312], we analyzed superconvergence for piecewise linear finite element approximations on triangular meshes where most pairs triangles sharing a common edge form approximate parallelograms. work, consider general unstructured but shape regular meshes. We develop postprocessing gradient recovery scheme the solution uh, inspired in part by smoothing iteration multigrid method. This recovered superconverges to true and becomes basis global posteriori error estimate that is often asymptotically exact. Next, use superconvergent Hessian matrix local indicators adaptive meshing algorithms. provide several numerical examples illustrating effectiveness our procedures.