Geodesic
About Delaunay triangulations and discrete maximum principles for the linear conforming FEM applied to the Poisson equation
Applications of Mathematics, Tome 46 (2001) no. 1, pp. 13-28.

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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.
DOI : 10.1023/A:1013775420323
Classification : 35J05, 65N30, 65N50
Keywords: linear conforming finite element method; Delaunay triangulation; discrete maximum principle 
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Vanselow, Reiner. About Delaunay triangulations and discrete maximum principles for the linear conforming FEM applied to the Poisson equation. Applications of Mathematics, Tome 46 (2001) no. 1, pp. 13-28. doi : 10.1023/A:1013775420323. http://geodesic.mathdoc.fr/articles/10.1023/A:1013775420323/

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