The discrete maximum principle for Galerkin solutions of elliptic problems
نویسنده
چکیده
This paper provides 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 arbitrarily dimensional simplices. The paper surveys the state of the art in the field of the discrete maximum principles and provide new generalizations of several results.
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