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Multilevel methods for elliptic problems on domains not resolved by the coarse grid. (English) Zbl 0817.65109

Keyes, David E. (ed.) et al., Domain decomposition methods in scientific and engineering computing. Proceedings of the 7th international conference on domain decomposition, October 27-30, 1993, Pennsylvania State University, PA, USA. Providence, RI: American Mathematical Society. Contemp. Math. 180, 49-60 (1994).
Summary: Elliptic boundary value problems are frequently posed on complicated domains, which cannot be covered by a simple coarse initial grid as is needed for multigrid-like iterative methods. In the present article, this problem is resolved for selfadjoint second-order problems and Dirichlet boundary conditions. The idea is to construct appropriate subspace decompositions of the corresponding finite element spaces by way of an embedding of the domain under consideration into a simpler domain like a square or a cube. Then the general theory of subspace correction methods can be applied.
For the entire collection see [Zbl 0809.00026].

MSC:

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