| Title:
|
About Delaunay triangulations and discrete maximum principles for the linear conforming FEM applied to the Poisson equation (English) |
| Author:
|
Vanselow, Reiner |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
46 |
| Issue:
|
1 |
| Year:
|
2001 |
| Pages:
|
13-28 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
linear conforming finite element method |
| Keyword:
|
Delaunay triangulation |
| Keyword:
|
discrete maximum principle |
| MSC:
|
35J05 |
| MSC:
|
65N30 |
| MSC:
|
65N50 |
| idZBL:
|
Zbl 1066.65132 |
| idMR:
|
MR1808427 |
| DOI:
|
10.1023/A:1013775420323 |
| . |
| Date available:
|
2009-09-22T18:05:36Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134456 |
| . |
| Reference:
|
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| Reference:
|
[2] D. Braess: Finite Elemente.Springer-Verlag, Berlin, 1992. Zbl 0754.65084 |
| Reference:
|
[3] F. Brezzi, M. Fortin: Mixed and Hybrid Finite Element Methods.Springer-Verlag, New York, 1991. MR 1115205 |
| Reference:
|
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| Reference:
|
[5] Ch. Großmann, H.-G. Roos: Numerik partieller Differentialgleichungen.Teubner, Stuttgart, 1992. MR 1219087 |
| Reference:
|
[6] F. Kratsch, H.-G. Roos: Diskrete Maximumprinzipien und deren Anwendung.Preprint 07-02-87, TU Dresden, 1987. |
| Reference:
|
[7] F. P. Preparata, M. I. Shamos: Computational Geometry. An Introduction.Springer-Verlag, New York, 1985. MR 0805539 |
| Reference:
|
[8] V. Ruas Santos: 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. MR 0672072 |
| Reference:
|
[9] R. Vanselow: Relations between FEM and FVM applied to the Poisson equation.Computing 57 (1996), 93–104. Zbl 0858.65109, MR 1407346, 10.1007/BF02276874 |
| Reference:
|
[10] G. Windisch: M-Matrices in Numerical Analysis.Teubner, Leipzig, 1989. MR 1059459 |
| . |
