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Numerische Mathematik

, Volume 88, Issue 2, pp 237–253 | Cite as

A primal mixed formulation for exterior transmission problems in ${\bf R}^2$

  • Gabriel R. Barrenechea
  • Gabriel N. Gatica
Orignial article

Summary.

We combine a primal mixed finite element approach with a Dirichlet-to-Neumann mapping (arising from the boundary integral equation method) to study the weak solvability and Galerkin approximations of a class of linear exterior transmission problems in potential theory. Our results are mainly based on the Babuska-Brezzi theory for variational problems with constraints. We establish the uniqueness of solution for the continuous and discrete formulations, and show that finite element subspac es of Lagrange type satisfy the discrete compatibility conditions. In addition, we provide the error analysis, including polygonal approximations of the domain, and prove strong convergence of the Galerkin solutions. Moreover, under additional regularity assumptions on the solution of the continuous formulation, we obtain the asymptotic rate of convergence O(h).

Mathematics Subject Classification (1991): 65N30, 65R20 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Gabriel R. Barrenechea
    • 1
  • Gabriel N. Gatica
    • 1
  1. 1.Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile; e-mail: {gbarrene,ggatica}@ing-mat.udec.cl CL

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