Volume 28, Issue 1
Superconvergence of Gradient Recovery Schemes on Graded Meshes for Corner Singularities

J. Comp. Math., 28 (2010), pp. 11-31.

Published online: 2010-02

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• Abstract

For the linear finite element solution to the Poisson equation, we show that superconvergence exists for a type of graded meshes for corner singularities in polygonal domains. In particular, we prove that the L^(2)-projection from the piecewise constant field to the continuous and piecewise linear finite element space gives a better approximation in the H^(1)-norm. In contrast to the existing superconvergence results, we do not assume high regularity of the exact solution.

• Keywords

Superconvergence Graded meshes Weighted Sobolev spaces Singular solutions The finite element method Gradient recovery schemes

• AMS Subject Headings

65N12 65N30 65N50.