Hessian Recovery for Finite Element Methods

2014/06/12 by Hailong Guo, Zhimin Zhang, Guo, Hailong +3 · 1 citation
Engineering · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods

paper · pdf · doi:10.48550/arxiv.1406.3108

Abstract

In this article, we propose and analyze an effective Hessian recovery strategy for the Lagrangian finite element of arbitrary order k. We prove that the proposed Hessian recovery preserves polynomials of degree k+1 on general unstructured meshes and superconverges at rate O(h^k) on mildly structured meshes. In addition, the method preserves polynomials of degree k+2 on translation invariant meshes and produces a symmetric Hessian matrix when the sampling points for recovery are selected with symmetry. Numerical examples are presented to support our theoretical results.

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