About Delaunay triangulations and discrete maximum principles for the linear conforming FEM applied to the Poisson equation

Reiner Vanselow

Applications of Mathematics (2001)

  • Volume: 46, Issue: 1, page 13-28
  • ISSN: 0862-7940

Abstract

top
The starting point of the analysis in this paper is the following situation: “In a bounded domain in 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.

How to cite

top

Vanselow, Reiner. "About Delaunay triangulations and discrete maximum principles for the linear conforming FEM applied to the Poisson equation." Applications of Mathematics 46.1 (2001): 13-28. <http://eudml.org/doc/33075>.

@article{Vanselow2001,
abstract = {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.},
author = {Vanselow, Reiner},
journal = {Applications of Mathematics},
keywords = {linear conforming finite element method; Delaunay triangulation; discrete maximum principle; linear conforming finite element method; Delaunay triangulation; discrete maximum principle},
language = {eng},
number = {1},
pages = {13-28},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {About Delaunay triangulations and discrete maximum principles for the linear conforming FEM applied to the Poisson equation},
url = {http://eudml.org/doc/33075},
volume = {46},
year = {2001},
}

TY - JOUR
AU - Vanselow, Reiner
TI - About Delaunay triangulations and discrete maximum principles for the linear conforming FEM applied to the Poisson equation
JO - Applications of Mathematics
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 46
IS - 1
SP - 13
EP - 28
AB - 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.
LA - eng
KW - linear conforming finite element method; Delaunay triangulation; discrete maximum principle; linear conforming finite element method; Delaunay triangulation; discrete maximum principle
UR - http://eudml.org/doc/33075
ER -

References

top
  1. An Introduction to Finite Volume Methods for Linear Elliptic Equations of Second Order, Preprint No. 164, Universität Erlangen-Nürnberg, Institut für Angewandte Mathematik I, 1995. (1995) MR1370105
  2. Finite Elemente, Springer-Verlag, Berlin, 1992. (1992) Zbl0754.65084
  3. Mixed and Hybrid Finite Element Methods, Springer-Verlag, New York, 1991. (1991) MR1115205
  4. A constrained two-dimensional triangulation and the solution of closest node problems in the presence of barriers, SIAM J. Numer. Anal. 27 (1990), 1305–1321. (1990) MR1061131
  5. Numerik partieller Differentialgleichungen, Teubner, Stuttgart, 1992. (1992) MR1219087
  6. Diskrete Maximumprinzipien und deren Anwendung, Preprint 07-02-87, TU Dresden, 1987. (1987) 
  7. Computational Geometry. An Introduction, Springer-Verlag, New York, 1985. (1985) MR0805539
  8. On the strong maximum principle for some piecewise linear finite element approximate problems of nonpositive type, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 29 (1982), 473–491. (1982) MR0672072
  9. 10.1007/BF02276874, Computing 57 (1996), 93–104. (1996) Zbl0858.65109MR1407346DOI10.1007/BF02276874
  10. M-Matrices in Numerical Analysis, Teubner, Leipzig, 1989. (1989) MR1059459

NotesEmbed ?

top

You must be logged in to post comments.