A weak discrete maximum principle for hp-FEM

Journal article

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 Höhn 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. © 2006 Elsevier B.V. All rights reserved.

Authors: Šolín, P; Vejchodský, T

• Journal: Journal of Computational and Applied Mathematics
• Volume: 209
• Issue: 1
• Pages: 54-65
• Publication date: 2007-12-01
• DOI: 10.1016/j.cam.2006.10.028
• ISSN: 0377-0427