Simplicial finite elements in higher dimensions

Jan Brandts; Sergey Korotov; Michal Křížek

Applications of Mathematics (2007)

  • Volume: 52, Issue: 3, page 251-265
  • ISSN: 0862-7940

Abstract

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Over the past fifty years, finite element methods for the approximation of solutions of partial differential equations (PDEs) have become a powerful and reliable tool. Theoretically, these methods are not restricted to PDEs formulated on physical domains up to dimension three. Although at present there does not seem to be a very high practical demand for finite element methods that use higher dimensional simplicial partitions, there are some advantages in studying the methods independent of the dimension. For instance, it provides additional insights into the structure and essence of proofs of results in one, two and three dimensions. In this survey paper we review some recent progress in this direction.

How to cite

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Brandts, Jan, Korotov, Sergey, and Křížek, Michal. "Simplicial finite elements in higher dimensions." Applications of Mathematics 52.3 (2007): 251-265. <http://eudml.org/doc/33287>.

@article{Brandts2007,
abstract = {Over the past fifty years, finite element methods for the approximation of solutions of partial differential equations (PDEs) have become a powerful and reliable tool. Theoretically, these methods are not restricted to PDEs formulated on physical domains up to dimension three. Although at present there does not seem to be a very high practical demand for finite element methods that use higher dimensional simplicial partitions, there are some advantages in studying the methods independent of the dimension. For instance, it provides additional insights into the structure and essence of proofs of results in one, two and three dimensions. In this survey paper we review some recent progress in this direction.},
author = {Brandts, Jan, Korotov, Sergey, Křížek, Michal},
journal = {Applications of Mathematics},
keywords = {$n$-simplex; finite element method; superconvergence; strengthened Cauchy-Schwarz inequality; discrete maximum principle; -simplex; finite element method; superconvergence; strengthened Cauchy-Schwarz inequality; discrete maximum principle; survey paper},
language = {eng},
number = {3},
pages = {251-265},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Simplicial finite elements in higher dimensions},
url = {http://eudml.org/doc/33287},
volume = {52},
year = {2007},
}

TY - JOUR
AU - Brandts, Jan
AU - Korotov, Sergey
AU - Křížek, Michal
TI - Simplicial finite elements in higher dimensions
JO - Applications of Mathematics
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 3
SP - 251
EP - 265
AB - Over the past fifty years, finite element methods for the approximation of solutions of partial differential equations (PDEs) have become a powerful and reliable tool. Theoretically, these methods are not restricted to PDEs formulated on physical domains up to dimension three. Although at present there does not seem to be a very high practical demand for finite element methods that use higher dimensional simplicial partitions, there are some advantages in studying the methods independent of the dimension. For instance, it provides additional insights into the structure and essence of proofs of results in one, two and three dimensions. In this survey paper we review some recent progress in this direction.
LA - eng
KW - $n$-simplex; finite element method; superconvergence; strengthened Cauchy-Schwarz inequality; discrete maximum principle; -simplex; finite element method; superconvergence; strengthened Cauchy-Schwarz inequality; discrete maximum principle; survey paper
UR - http://eudml.org/doc/33287
ER -

References

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