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linear conforming finite element method; Delaunay triangulation; discrete maximum principle
The starting point of the analysis in this paper is the following situation: “In a bounded domain in $\mathbb{R}^2$, 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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