Some mixed finite element methods on anisotropic meshes
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 35 (2001) no. 5, p. 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
Keywords: 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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {35},
     number = {5},
     year = {2001},
     pages = {907-920},
     zbl = {0990.65129},
     mrnumber = {1866274},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2001__35_5_907_0}
}
Farhloul, Mohamed; Nicaise, Serge; Paquet, Luc. Some mixed finite element methods on anisotropic meshes. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 35 (2001) no. 5, pp. 907-920. http://www.numdam.org/item/M2AN_2001__35_5_907_0/

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