| Title:
|
Generalization of the Zlámal condition for simplicial finite elements in ${\Bbb R}^d$ (English) |
| Author:
|
Brandts, Jan |
| Author:
|
Korotov, Sergey |
| Author:
|
Křížek, Michal |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
56 |
| Issue:
|
4 |
| Year:
|
2011 |
| Pages:
|
417-424 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The famous Zlámal's minimum angle condition has been widely used for construction of a regular family of triangulations (containing nondegenerating triangles) as well as in convergence proofs for the finite element method in $2d$. In this paper we present and discuss its generalization to simplicial partitions in any space dimension. (English) |
| Keyword:
|
linear finite element |
| Keyword:
|
mesh regularity |
| Keyword:
|
minimum angle condition |
| Keyword:
|
convergence |
| Keyword:
|
higher-dimensional problems |
| Keyword:
|
triangulations |
| MSC:
|
65N12 |
| MSC:
|
65N30 |
| MSC:
|
65N50 |
| idZBL:
|
Zbl 1240.65327 |
| idMR:
|
MR2833170 |
| DOI:
|
10.1007/s10492-011-0024-1 |
| . |
| Date available:
|
2011-06-23T13:11:11Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141603 |
| . |
| Reference:
|
[1] Apel, T.: Anisotropic Finite Elements: Local Estimates and Applications. Advances in Numerical Mathematics.B. G. Teubner Leipzig (1999). MR 1716824 |
| Reference:
|
[2] Brandts, J., Korotov, S., Křížek, M.: On the equivalence of regularity criteria for triangular and tetrahedral finite element partitions.Comput. Math. Appl. 55 (2008), 2227-2233. Zbl 1142.65443, MR 2413688, 10.1016/j.camwa.2007.11.010 |
| Reference:
|
[3] Brandts, J., Korotov, S., Křížek, M.: On the equivalence of ball conditions for simplicial finite elements in ${\Bbb R}^d$.Appl. Math. Lett. 22 (2009), 1210-1212. MR 2532540, 10.1016/j.aml.2009.01.031 |
| Reference:
|
[4] Brandts, J., Křížek, M.: Gradient superconvergence on uniform simplicial partitions of polytopes.IMA J. Numer. Anal. 23 (2003), 489-505. Zbl 1042.65081, MR 1987941, 10.1093/imanum/23.3.489 |
| Reference:
|
[5] Ciarlet, P. G.: The Finite Element Method for Elliptic Problems.North-Holland Amsterdam (1978). Zbl 0383.65058, MR 0520174 |
| Reference:
|
[6] Eriksson, F.: The law of sines for tetrahedra and $n$-simplices.Geom. Dedicata 7 (1978), 71-80. Zbl 0375.50008, MR 0474009, 10.1007/BF00181352 |
| Reference:
|
[7] Hannukainen, A., Korotov, S., Křížek, M.: On global and local mesh refinements by a generalized conforming bisection algorithm.J. Comput. Appl. Math. 235 (2010), 419-436. Zbl 1207.65145, MR 2677699, 10.1016/j.cam.2010.05.046 |
| Reference:
|
[8] Lin, J., Lin, Q.: Global superconvergence of the mixed finite element methods for 2-D Maxwell equations.J. Comput. Math. 21 (2003), 637-646. Zbl 1032.65101, MR 1999974 |
| Reference:
|
[9] Rektorys, K.: Survey of Applicable Mathematics, Vol. 1.Kluwer Academic Publishers Dordrecht (1994). 10.1007/978-94-015-8308-4 |
| Reference:
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[10] Schewchuk, J. R.: What is a good linear finite element? Interpolation, conditioning, anisotropy, and quality measures.Preprint Univ. of California at Berkeley (2002), 1-66. MR 3190484 |
| Reference:
|
[11] Ženíšek, A.: The convergence of the finite element method for boundary value problems of a system of elliptic equations.Apl. Mat. 14 (1969), 355-377 Czech. MR 0245978 |
| Reference:
|
[12] Zlámal, M.: On the finite element method.Numer. Math. 12 (1968), 394-409. MR 0243753, 10.1007/BF02161362 |
| . |
