Some mixed finite element methods on anisotropic meshes

Mohamed Farhloul; Serge Nicaise[1]; Luc Paquet

  • [1] Université de Valenciennes et du Hainaut Cambrésis, MACS, Le Mont Houy, 59313 Valenciennes Cedex 9, France. http://www.univ-valenciennes.fr/macs/Serge.Nicaise

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2001)

  • Volume: 35, Issue: 5, page 907-920
  • ISSN: 0764-583X

Abstract

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The paper deals with some mixed finite element methods on a class of anisotropic meshes based on tetrahedra and prismatic (pentahedral) elements. Anisotropic local interpolation error estimates are derived in some anisotropic weighted Sobolev spaces. As particular applications, the numerical approximation by mixed methods of the Laplace equation in domains with edges is investigated where anisotropic finite element meshes are appropriate. Optimal error estimates are obtained using some anisotropic regularity results of the solutions.

How to cite

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Farhloul, Mohamed, Nicaise, Serge, and Paquet, Luc. "Some mixed finite element methods on anisotropic meshes." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 35.5 (2001): 907-920. <http://eudml.org/doc/194080>.

@article{Farhloul2001,
abstract = {The paper deals with some mixed finite element methods on a class of anisotropic meshes based on tetrahedra and prismatic (pentahedral) elements. Anisotropic local interpolation error estimates are derived in some anisotropic weighted Sobolev spaces. As particular applications, the numerical approximation by mixed methods of the Laplace equation in domains with edges is investigated where anisotropic finite element meshes are appropriate. Optimal error estimates are obtained using some anisotropic regularity results of the solutions.},
affiliation = {Université de Valenciennes et du Hainaut Cambrésis, MACS, Le Mont Houy, 59313 Valenciennes Cedex 9, France. http://www.univ-valenciennes.fr/macs/Serge.Nicaise},
author = {Farhloul, Mohamed, Nicaise, Serge, Paquet, Luc},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {anisotropic mesh; Raviart-Thomas element; anisotropic interpolation error estimate; Laplace equation; edge singularity; mixed FEM; mixed finite element methods; anisotropic meshes; error estimates},
language = {eng},
number = {5},
pages = {907-920},
publisher = {EDP-Sciences},
title = {Some mixed finite element methods on anisotropic meshes},
url = {http://eudml.org/doc/194080},
volume = {35},
year = {2001},
}

TY - JOUR
AU - Farhloul, Mohamed
AU - Nicaise, Serge
AU - Paquet, Luc
TI - Some mixed finite element methods on anisotropic meshes
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2001
PB - EDP-Sciences
VL - 35
IS - 5
SP - 907
EP - 920
AB - The paper deals with some mixed finite element methods on a class of anisotropic meshes based on tetrahedra and prismatic (pentahedral) elements. Anisotropic local interpolation error estimates are derived in some anisotropic weighted Sobolev spaces. As particular applications, the numerical approximation by mixed methods of the Laplace equation in domains with edges is investigated where anisotropic finite element meshes are appropriate. Optimal error estimates are obtained using some anisotropic regularity results of the solutions.
LA - eng
KW - anisotropic mesh; Raviart-Thomas element; anisotropic interpolation error estimate; Laplace equation; edge singularity; mixed FEM; mixed finite element methods; anisotropic meshes; error estimates
UR - http://eudml.org/doc/194080
ER -

References

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