The discrete maximum principle for Galerkin solutions of elliptic problems

0370385 - MÚ 2012 RIV PL eng J - Článek v odborném periodiku
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
Grant CEP: GA AV ČR IAA100760702
Výzkumný záměr: CEZ:AV0Z10190503
Klíčová slova: discrete maximum principle * monotone methods * Galerkin solution
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.405, rok: 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.
Trvalý link: http://hdl.handle.net/11104/0204209