Minimization of gradient errors of piecewise linear interpolation on simplicial meshes

被引：15

作者：

Agouzal, Abdellatif ^{[2
]}

Vassilevski, Yuri V. ^{[1
]}

机构：

[1] Russian Acad Sci, Inst Numer Math, Moscow 119333, Russia

[2] Univ Lyon 1, UMR 5585, Lab Analyse Numer, F-69622 Villeurbanne, France

来源：

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | 2010年 / 199卷 / 33-36期

基金：

俄罗斯基础研究基金会;

关键词：

Optimal mesh; Gradient interpolation error; Metric based adaptation;

D O I：

10.1016/j.cma.2010.03.019

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

The paper is devoted to the analysis of optimal simplicial meshes which minimize the gradient error of the piecewise linear interpolation over all conformal simplicial meshes with a fixed number of cells N-T. We present theoretical results on asymptotic dependencies of L-p-norms of the gradient error on N-T for spaces of arbitrary dimension d. Our analysis is based on a geometric representation of the gradient error of linear interpolation on a simplex and a relaxed saturation assumption. We derive a metric field M-p such that a M-p-quasi-uniform mesh is quasi-optimal, for arbitrary d and p is an element of]0, +infinity]. Quasi-optimal meshes provide the same asymptotics of the L-p-norm of the gradient error as the optimal meshes. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：2195 / 2203

页数：9