On a new edge‐based gradient recovery technique

Abstract

SUMMARY A posteriori error estimation methods for mesh adaptation often require an accurate computation of the gradient of a Lagrange finite element solution. The precision of the error estimation is directly related to the accuracy of the recovered gradient. We therefore present in this communication a simple method for the evaluation of the gradient of a linear Lagrange finite element solution, and we show that it has significant advantages over existing methods of the same order. The proposed method requires the solution of a global linear system that can be solved by a preconditioned conjugate gradient method. An interesting feature is that it does not require any special treatment for boundary nodes contrarily to classical local patch recovery methods. Copyright © 2012 John Wiley & Sons, Ltd.

Hessian recovery for finite element methods

“…These quantities of interest usually involve derivatives of the primary data. Some popular post-processing techniques include the celebrated Zienkiewicz-Zhu superconvergent patch recovery (SPR) [26], polynomial preserving recovery (PPR) [25,15], and edge based recovery [19], which were proposed to obtain accurate gradients with reasonable cost. Similarly, post-processing for second order derivatives, which are related to physical quantities such as momentum and Hessian, are also desirable.…”

Polynomial preserving recovery on boundary

“…Introduction. Gradient recovery [7,10,12,17,[20][21][22][23][24][25] is an effective and widely used post-processing technique in scientific and engineering computation. The main purpose of this techniques is to reconstruct a better numerical gradient from a finite element solution.…”

A postprocessed flux conserving finite element solution

“…Nevertheless, the flux can be lost between macro elements. As our correction of finite element solution is guided by super‐convergent point flux values, the idea is used recently by Pouliot et al who solve a global L 2 system to recover a high‐order convergent flux from supconvergent point values.…”