On Synge-type angle condition for d -simplices

Antti Hannukainen; Sergey Korotov; Michal Křížek

Applications of Mathematics (2017)

  • Volume: 62, Issue: 1, page 1-13
  • ISSN: 0862-7940

Abstract

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The maximum angle condition of J. L. Synge was originally introduced in interpolation theory and further used in finite element analysis and applications for triangular and later also for tetrahedral finite element meshes. In this paper we present some of its generalizations to higher-dimensional simplicial elements. In particular, we prove optimal interpolation properties of linear simplicial elements in ℝ d that degenerate in some way.

How to cite

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Hannukainen, Antti, Korotov, Sergey, and Křížek, Michal. "On Synge-type angle condition for $d$-simplices." Applications of Mathematics 62.1 (2017): 1-13. <http://eudml.org/doc/287566>.

@article{Hannukainen2017,
abstract = {The maximum angle condition of J. L. Synge was originally introduced in interpolation theory and further used in finite element analysis and applications for triangular and later also for tetrahedral finite element meshes. In this paper we present some of its generalizations to higher-dimensional simplicial elements. In particular, we prove optimal interpolation properties of linear simplicial elements in $\{\mathbb \{R\}\}^d$ that degenerate in some way.},
author = {Hannukainen, Antti, Korotov, Sergey, Křížek, Michal},
journal = {Applications of Mathematics},
keywords = {simplicial element; maximum angle condition; interpolation error; higher-dimensional problem; $d$-dimensional sine; semiregular family of simplicial partitions; Poisson equation; numerical examples; maximum angle condition; finite element; optimal convergence rate; elliptic problems},
language = {eng},
number = {1},
pages = {1-13},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On Synge-type angle condition for $d$-simplices},
url = {http://eudml.org/doc/287566},
volume = {62},
year = {2017},
}

TY - JOUR
AU - Hannukainen, Antti
AU - Korotov, Sergey
AU - Křížek, Michal
TI - On Synge-type angle condition for $d$-simplices
JO - Applications of Mathematics
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 1
SP - 1
EP - 13
AB - The maximum angle condition of J. L. Synge was originally introduced in interpolation theory and further used in finite element analysis and applications for triangular and later also for tetrahedral finite element meshes. In this paper we present some of its generalizations to higher-dimensional simplicial elements. In particular, we prove optimal interpolation properties of linear simplicial elements in ${\mathbb {R}}^d$ that degenerate in some way.
LA - eng
KW - simplicial element; maximum angle condition; interpolation error; higher-dimensional problem; $d$-dimensional sine; semiregular family of simplicial partitions; Poisson equation; numerical examples; maximum angle condition; finite element; optimal convergence rate; elliptic problems
UR - http://eudml.org/doc/287566
ER -

References

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