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A Schwarz alternating algorithm for elliptic boundary value problems in an infinite domain with a concave angle. (English) Zbl 1071.65171

The authors study a Schwarz iterative algorithm used to solve elliptic boundary value problems formulated upon an infinite domain with a concave angle. The introduction of two artificial boundaries allows to solve the original problem in a bounded domain by a standard finite element method and in an unbounded domain by the natural boundary element method. The convergence of the resulting algorithm is carefully analyzed and some numerical experiments prove the effectiveness of the method.

MSC:

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N38 Boundary element methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65F10 Iterative numerical methods for linear systems
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References:

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