Adaptive mixed hybrid and macro-hybrid finite element methods.
Hoppe, R.H.W., Wohlmuth, B.I. (1998)
Acta Mathematica Universitatis Comenianae. New Series
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Hoppe, R.H.W., Wohlmuth, B.I. (1998)
Acta Mathematica Universitatis Comenianae. New Series
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Mauricio A. Barrientos, Gabriel N. Gatica, Matthias Maischak (2002)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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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, and...
Francesca Gardini (2009)
ESAIM: Mathematical Modelling and Numerical Analysis
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We state a superconvergence result for the lowest order Raviart-Thomas approximation of eigenvalue problems. It is known that a similar superconvergence result holds for the mixed approximation of Laplace problem; here we introduce a new proof, since the one given for the source problem cannot be generalized in a straightforward way to the eigenvalue problem. Numerical experiments confirm the superconvergence property and suggest that it also holds for the lowest order Brezzi-Douglas-Marini...
Mohamed Farhloul, Serge Nicaise, Luc Paquet (2001)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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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 some...