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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 derive the...
We give details of the theory of primal domain decomposition (DD) methods for a 2-dimensional second order elliptic equation with homogeneous Dirichlet boundary conditions and jumping coefficients. The problem is discretized by the finite element method. The computational domain is decomposed into triangular subdomains that align with the coefficients jumps. We prove that the condition number of the vertex-based DD preconditioner is , independently of the coefficient jumps, where and denote...
This paper deals with the solution of problems involving partial differential
equations in . 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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