Some mixed finite element methods on anisotropic meshes

Farhloul, Mohamed; Nicaise, Serge; Paquet, Luc

ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 5, pp. 907-920.

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.

Classification : 65N30, 65N15, 65N50, 65D05
Mots clés : anisotropic mesh, Raviart-Thomas element, anisotropic interpolation error estimate, Laplace equation, edge singularity, mixed FEM

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