Asymptotically exact a posteriori error estimators, Part II: General unstructured grids

被引:39
作者
Bank, RE [1 ]
Xu, JC
机构
[1] Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA
[2] Penn State Univ, Dept Math, Ctr Computat Math & Applicat, University Pk, PA 16802 USA
关键词
superconvergence; gradient recovery; a posteriori error estimates;
D O I
10.1137/S0036142901398751
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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 of triangles sharing a common edge form approximate parallelograms. In this work, we consider superconvergence for general unstructured but shape regular meshes. We develop a postprocessing gradient recovery scheme for the finite element solution u(h), inspired in part by the smoothing iteration of the multigrid method. This recovered gradient superconverges to the gradient of the true solution and becomes the basis of a global a posteriori error estimate that is often asymptotically exact. Next, we use the superconvergent gradient to approximate the Hessian matrix of the true solution and form local error indicators for adaptive meshing algorithms. We provide several numerical examples illustrating the effectiveness of our procedures.
引用
收藏
页码:2313 / 2332
页数:20
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