Applications of Mathematics

, Volume 46, Issue 1, pp 13–28

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

  • Reiner Vanselow

DOI: 10.1023/A:1013775420323

Cite this article as:
Vanselow, R. Applications of Mathematics (2001) 46: 13. doi:10.1023/A:1013775420323


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.

linear conforming finite element methodDelaunay triangulationdiscrete maximum principle

Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2001

Authors and Affiliations

  • Reiner Vanselow
    • 1
  1. 1.Institut fur Numerische MathematikTechnische Universitat Dresden, Mommsenstrasse 13DresdenGermany