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A Two-mesh Superconvergence Method for Mesh Adaptivity

A two-mesh superconvergent gradient recovery mechanism for elliptic equations is presented. The method first computes the gradient over a fine mesh and then project it to a coarser mesh. This projected gradient has superconvergence properties for general unstructured meshes. The difference between the computed and projected gradient is used as the error indicator in refining a mesh adaptively. This new superconvergence mesh refinement technique is easy to implement and can be used for a large class of problems. Numerical experiments for smooth and singular elliptic problems given in this work show the efficiency of this technique. Comparisons with a classical mesh adaptivity method is also given here to show the advantages.