Displaying similar documents to “The mixed problem for the Laplace equation on the rectangle”

Some mixed finite element methods on anisotropic meshes

Mohamed Farhloul, Serge Nicaise, Luc Paquet (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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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...

error estimates for linear exterior problems mixed-FEM and DtN mappings

Mauricio A. Barrientos, Gabriel N. Gatica, Matthias Maischak (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper we combine the dual-mixed finite element method with a Dirichlet-to-Neumann mapping (given in terms of a boundary integral operator) to solve linear exterior transmission problems in the plane. As a model we consider a second order elliptic equation in divergence form coupled with the Laplace equation in the exterior unbounded region. We show that the resulting mixed variational formulation and an associated discrete scheme using Raviart-Thomas spaces are well posed,...

Error Estimates For the D Stabilized Mortar Finite Element Method applied to the Laplace Equation

Zakaria Belhachmi (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We consider a non-conforming stabilized domain decomposition technique for the discretization of the three-dimensional Laplace equation. The aim is to extend the numerical analysis of residual error indicators to this model problem. Two formulations of the problem are considered and the error estimators are studied for both. In the first one, the error estimator provides upper and lower bounds for the energy norm of the mortar finite element solution whereas in the second case, it also...