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

top
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

top

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

top
  1. Apel, T., Anisotropic Finite Elements: Local Estimates and Applications. Advances in Numerical Mathematics, B. G. Teubner Leipzig (1999). (1999) MR1716824
  2. Brandts, J., Korotov, S., Křížek, M., 10.1016/j.camwa.2007.11.010, Comput. Math. Appl. 55 (2008), 2227-2233. (2008) Zbl1142.65443MR2413688DOI10.1016/j.camwa.2007.11.010
  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
  6. Eriksson, F., 10.1007/BF00181352, Geom. Dedicata 7 (1978), 71-80. (1978) Zbl0375.50008MR0474009DOI10.1007/BF00181352
  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

NotesEmbed ?

top

You must be logged in to post comments.