Discrete Conservation of Nonnegativity for Elliptic Problems Solved by the hp-FEM

Authors

Pavel Solin
Thomas Vejchodsky
Roberto Araiza, The University of Texas at El PasoFollow

Publication Date

8-2005

Comments

UTEP-CS-05-29.

Published in Mathematics and Computers in Simulation, 2007, Vol. 76, pp. 205-210.

Abstract

Most results related to discrete nonnegativity conservation principles (DNCP) for elliptic problems are limited to finite differences (FDM) and lowest-order finite element methods (FEM). In this paper we confirm that a straightforward extension to higher-order finite element methods (hp-FEM) in the classical sense is not possible. We formulate a weaker DNCP for the Poisson equation in one spatial dimension and prove it using an interval computing technique. Numerical experiments related to the extension of this result to 2D are presented.