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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.

Reviewer: Michel Bernadou (Paris La Defense)

### 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 |

### Keywords:

Infinite domain; Concave angle; Schwarz alternating algorithm; Artificial boundary; Iteration method; elliptic boundary value problems; finite element method; boundary element method; convergence; numerical experiments
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\textit{M. Yang} and \textit{Q. Du}, Appl. Math. Comput. 159, No. 1, 199--220 (2004; Zbl 1071.65171)

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### References:

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