| Issue |
ESAIM: M2AN
Volume 35, Number 5, September-October 2001
|
|
|---|---|---|
| Page(s) | 907 - 920 | |
| DOI | https://doi.org/10.1051/m2an:2001142 | |
| Published online | 15 April 2002 | |
Some mixed finite element methods on anisotropic meshes
1
Université de Moncton, Département de Mathématiques et de
Statistique, N.B., E1A 3 E9,
Moncton, Canada. (farhlom@umoncton.ca)
2
Université de Valenciennes et du Hainaut Cambrésis,
MACS, ISTV, 59313 Valenciennes Cedex 9, France. (snicaise@univ-valenciennes.fr),
3
Université de Valenciennes et du Hainaut Cambrésis,
MACS, ISTV, 59313 Valenciennes Cedex 9, France. (Luc.Paquet@univ-valenciennes.fr)
Received:
26
February
2001
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.
Mathematics Subject Classification: 65N30 / 65N15 / 65N50 / 65D05
Key words: Anisotropic mesh / Raviart-Thomas element / anisotropic interpolation error estimate / Laplace equation / edge singularity / mixed FEM.
© EDP Sciences, SMAI, 2001
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