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

Mauricio A. Barrientos, Gabriel N. Gatica, Matthias Maischak (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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 derive the...

3D domain decomposition method coupling conforming and nonconforming finite elements

Abdellatif Agouzal, Laurence Lamoulie, Jean-Marie Thomas (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper deals with the solution of problems involving partial differential equations in  ℝ 3 . For three dimensional case, methods are useful if they require neither domain boundary regularity nor regularity for the exact solution of the problem. A new domain decomposition method is therefore presented which uses low degree finite elements. The numerical approximation of the solution is easy, and optimal error bounds are obtained according to suitable norms.

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