Generalization of the Zlámal condition for simplicial finite elements in ℝ d

Jan Brandts; Sergey Korotov; Michal Křížek

Applications of Mathematics (2011)

  • Volume: 56, Issue: 4, page 417-424
  • ISSN: 0862-7940

Abstract

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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 2 d . In this paper we present and discuss its generalization to simplicial partitions in any space dimension.

How to cite

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Brandts, Jan, Korotov, Sergey, and Křížek, Michal. "Generalization of the Zlámal condition for simplicial finite elements in ${\mathbb {R}}^d$." Applications of Mathematics 56.4 (2011): 417-424. <http://eudml.org/doc/116548>.

@article{Brandts2011,
abstract = {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.},
author = {Brandts, Jan, Korotov, Sergey, Křížek, Michal},
journal = {Applications of Mathematics},
keywords = {linear finite element; mesh regularity; minimum angle condition; convergence; higher-dimensional problems; triangulations; linear finite element; mesh regularity; minimum angle condition; convergence; higher-dimensional problem; triangulations},
language = {eng},
number = {4},
pages = {417-424},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Generalization of the Zlámal condition for simplicial finite elements in $\{\mathbb \{R\}\}^d$},
url = {http://eudml.org/doc/116548},
volume = {56},
year = {2011},
}

TY - JOUR
AU - Brandts, Jan
AU - Korotov, Sergey
AU - Křížek, Michal
TI - Generalization of the Zlámal condition for simplicial finite elements in ${\mathbb {R}}^d$
JO - Applications of Mathematics
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 4
SP - 417
EP - 424
AB - 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.
LA - eng
KW - linear finite element; mesh regularity; minimum angle condition; convergence; higher-dimensional problems; triangulations; linear finite element; mesh regularity; minimum angle condition; convergence; higher-dimensional problem; triangulations
UR - http://eudml.org/doc/116548
ER -

References

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  3. Brandts, J., Korotov, S., Křížek, M., 10.1016/j.aml.2009.01.031, Appl. Math. Lett. 22 (2009), 1210-1212. (2009) MR2532540DOI10.1016/j.aml.2009.01.031
  4. Brandts, J., Křížek, M., 10.1093/imanum/23.3.489, IMA J. Numer. Anal. 23 (2003), 489-505. (2003) Zbl1042.65081MR1987941DOI10.1093/imanum/23.3.489
  5. Ciarlet, P. G., The Finite Element Method for Elliptic Problems, North-Holland Amsterdam (1978). (1978) Zbl0383.65058MR0520174
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  7. Hannukainen, A., Korotov, S., Křížek, M., 10.1016/j.cam.2010.05.046, J. Comput. Appl. Math. 235 (2010), 419-436. (2010) Zbl1207.65145MR2677699DOI10.1016/j.cam.2010.05.046
  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. (2003) Zbl1032.65101MR1999974
  9. Rektorys, K., 10.1007/978-94-015-8308-4, Kluwer Academic Publishers Dordrecht (1994). (1994) DOI10.1007/978-94-015-8308-4
  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. (2002) MR3190484
  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. (1969) MR0245978
  12. Zlámal, M., 10.1007/BF02161362, Numer. Math. 12 (1968), 394-409. (1968) MR0243753DOI10.1007/BF02161362

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