Discrete conservation of nonnegativity for elliptic problems solved by the hp-FEM

Pavel Šolín, Tomáš Vejchodský and Roberto Araiza

Mathematics and Computers in Simulation (MATCOM), 2007, vol. 76, issue 1, 205-210

Abstract: Most results related to discrete nonnegativity conservation principles (DNCP) for elliptic problems are limited to finite differences and lowest-order finite element methods (FEM). In this paper we show 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.

Keywords: Discrete nonnegativity conservation; Discrete Green’s function; Elliptic problems; hp-FEM (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:76:y:2007:i:1:p:205-210

DOI: 10.1016/j.matcom.2007.01.015

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