The discrete maximum principle for Galerkin solutions of elliptic problems

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 appl...

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Bibliographic Details
Published in:Central European journal of mathematics 2012-02, Vol.10 (1), p.25-43
Main Author: Vejchodský, Tomáš
Format: Article
Language:English
Subjects:
35B50
65N30
Algebra
Discrete maximum principle
Finite element metho
Galerkin method
Galerkin solution
Geometry
Lie Groups
Mathematics
Mathematics and Statistics
Maximum principle
Monotone methods
Number Theory
Probability Theory and Stochastic Processes
Research Article
Topological Groups
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Summary: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.
ISSN:1895-1074
1644-3616
2391-5455
DOI:10.2478/s11533-011-0085-0