Published

Superconvergence of Gradient Recovery Schemes on graded meshes for corner singularities

Long Chen and Hengguang Li

Journal of Computational Mathematics, 28, 11-31.

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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
    $\nabla u_N$ to the continuous and piecewise linear finite element
    space gives a better approximation of $\nabla u$ in the
    $H^1$-norm. In contrast to the existing superconvergence results,
    we do not assume high regularity of the exact solution.