A weak discrete maximum principle for hp-FEM

被引：11

作者：

Solin, Pavel ^{[1
,3
]}

Vejchodsky, Tomas ^{[2
]}

机构：

[1] Univ Texas El Paso, Dept Math Sci, El Paso, TX 79968 USA

[2] Acad Sci, Math Inst, Prague 11567 1, Czech Republic

[3] Acad Sci Czech Republ, Inst Thermomech, Prague 18200 8, Czech Republic

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2007年 / 209卷 / 01期

基金：

美国国家科学基金会;

关键词：

discrete maximum principle; Poisson equation; hp-FEM; higher-order elements;

D O I：

10.1016/j.cam.2006.10.028

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we prove a new discrete maximum principle (DMP) for the one-dimensional Poisson equation discretized by the hp-FEM. While the DMP for piecewise-linear elements is a classical result from the 1970s, no extensions to hp-FEM are available to the present day. Due to a negative result by Hohn and Mittelmann from 1981, related to quadratic Lagrange elements, it was long assumed that higher-order finite elements do not satisfy discrete maximum principles. In this paper we explain why it is not possible to make a straightforward extension of the classical DMP to the higher-order case, and we propose stronger assumptions on the right-hand side under which an extension is possible. (c) 2006 Elsevier B.V. All rights reserved.

引用

页码：54 / 65

页数：12

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