Asymptotic Expansions and L...-Error Estimates for Mixed Finite Element Methods for Second Order Elliptic Problems.
Junping Wang (1987)
Numerische Mathematik
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Junping Wang (1987)
Numerische Mathematik
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Aihui Zhou (1999)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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Jan Brandts (1999)
Applications of Mathematics
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We will investigate the possibility to use superconvergence results for the mixed finite element discretizations of some time-dependent partial differential equations in the construction of a posteriori error estimators. Since essentially the same approach can be followed in two space dimensions, we will, for simplicity, consider a model problem in one space dimension.
Christine Bernardi, Frédéric Hecht (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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For the Stokes problem in a two- or three-dimensional bounded domain, we propose a new mixed finite element discretization which relies on a nonconforming approximation of the velocity and a more accurate approximation of the pressure. We prove that the velocity and pressure discrete spaces are compatible, in the sense that they satisfy an inf-sup condition of Babuška and Brezzi type, and we derive some error estimates.
Franco Brezzi, Jim, Jr. Douglas (1988)
Numerische Mathematik
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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...
P.M. Hanson, J.E. Walsh (1984)
Numerische Mathematik
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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...