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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:
65N55Multigrid methods; domain decomposition (BVP of PDE)
65N12Stability and convergence of numerical methods (BVP of PDE)
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
65N38Boundary element methods (BVP of PDE)
35J25Second order elliptic equations, boundary value problems
65F10Iterative methods for linear systems