The discrete maximum principle for Galerkin solutions of elliptic problems

0370385 - MÚ 2012 RIV PL eng J - Journal Article
Vejchodský, Tomáš
The discrete maximum principle for Galerkin solutions of elliptic problems.
Central European Journal of Mathematics. Roč. 10, č. 1 (2012), s. 25-43. ISSN 1895-1074
R&D Projects: GA AV ČR IAA100760702
Institutional research plan: CEZ:AV0Z10190503
Keywords : discrete maximum principle * monotone methods * Galerkin solution
Subject RIV: BA - General Mathematics
Impact factor: 0.405, year: 2012
http://www.springerlink.com/content/x73624wm23x4wj26

This paper provides an equivalent characterization of the discrete maximum principle for Galerkin solutions of general linear elliptic problems. The characterization is formulated in terms of the discrete Green’s function and the elliptic projection of the boundary data. This general concept is applied to the analysis of the discrete maximum principle for the higher-order finite elements in one-dimension and to the lowest-order finite elements on simplices of arbitrary dimension. The paper surveys the state of the art in the field of the discrete maximum principle and provides new generalizations of several results.
Permanent Link: http://hdl.handle.net/11104/0204209