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About Delaunay Triangulations and Discrete Maximum Principles for the Linear Conforming FEM Applied to the Poisson Equation

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Abstract

The starting point of the analysis in this paper is the following situation: "In a bounded domain in ℝ2, let a finite set of points be given. A triangulation of that domain has to be found, whose vertices are the given points and which is `suitable' for the linear conforming Finite Element Method (FEM)." The result of this paper is that for the discrete Poisson equation and under some weak additional assumptions, only the use of Delaunay triangulations preserves the maximum principle.

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  1. Institut fur Numerische Mathematik, Technische Universitat Dresden, Mommsenstrasse 13, 01062, Dresden, Germany

    Reiner Vanselow

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  1. Reiner Vanselow
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Vanselow, R. About Delaunay Triangulations and Discrete Maximum Principles for the Linear Conforming FEM Applied to the Poisson Equation. Applications of Mathematics 46, 13–28 (2001). https://doi.org/10.1023/A:1013775420323

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  • DOI: https://doi.org/10.1023/A:1013775420323

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