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.
Mots-clés : anisotropic mesh, Raviart-Thomas element, anisotropic interpolation error estimate, Laplace equation, edge singularity, mixed FEM
@article{M2AN_2001__35_5_907_0, author = {Farhloul, Mohamed and Nicaise, Serge and Paquet, Luc}, title = {Some mixed finite element methods on anisotropic meshes}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {907--920}, publisher = {EDP-Sciences}, volume = {35}, number = {5}, year = {2001}, mrnumber = {1866274}, zbl = {0990.65129}, language = {en}, url = {http://archive.numdam.org/item/M2AN_2001__35_5_907_0/} }
TY - JOUR AU - Farhloul, Mohamed AU - Nicaise, Serge AU - Paquet, Luc TI - Some mixed finite element methods on anisotropic meshes JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2001 SP - 907 EP - 920 VL - 35 IS - 5 PB - EDP-Sciences UR - http://archive.numdam.org/item/M2AN_2001__35_5_907_0/ LA - en ID - M2AN_2001__35_5_907_0 ER -
%0 Journal Article %A Farhloul, Mohamed %A Nicaise, Serge %A Paquet, Luc %T Some mixed finite element methods on anisotropic meshes %J ESAIM: Modélisation mathématique et analyse numérique %D 2001 %P 907-920 %V 35 %N 5 %I EDP-Sciences %U http://archive.numdam.org/item/M2AN_2001__35_5_907_0/ %G en %F M2AN_2001__35_5_907_0
Farhloul, Mohamed; Nicaise, Serge; Paquet, Luc. Some mixed finite element methods on anisotropic meshes. ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 5, pp. 907-920. http://archive.numdam.org/item/M2AN_2001__35_5_907_0/
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