HESSIAN RECOVERY FOR FINITE ELEMENT METHODS
Hailong Guo, Zhimin Zhang, Ren Zhao
MATHEMATICS OF COMPUTATION | AMER MATHEMATICAL SOC | Published : 2017
In this article, we propose and analyze an effective Hessian recovery strategy for the Lagrangian finite element method of arbitrary order. We prove that the proposed Hessian recovery method preserves polynomials of degree k + 1 on general unstructured meshes and superconverges at a rate of O(hk) on mildly structured meshes. In addition, the method is proved to be ultraconvergent (two orders higher) for the translation invariant finite element space of any order. Numerical examples are presented to support our theoretical results.
Awarded by National Natural Science Foundation of China
Awarded by U.S. National Science Foundation
The second author is the corresponding author. The research of the second author was supported in part by the National Natural Science Foundation of China under grants 11471031, 91430216 U1530401, and the U.S. National Science Foundation through grant DMS-1419040.