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Multilevel additive Schwarz preconditioner for nonconforming mortar finite element methods. (English) Zbl 1050.65048

The authors discuss a multilevel preconditionier for mortar finite elements on non-matching triangulations. A characteristic feature of mortar methods is that subdomain meshes may be constructed separately in each subdomain and are, in general, non-matching along the interfaces, in contrast to traditional decomposition methods, where a globally conforming triangulation is used. The main result consists in an upper bound for the condition number of the additive Schwarz operator, in terms of the refinement level. Numerical examples are performed and the performance of the multilevel additive Schwarz method is illustrated.

MSC:

65F35 Numerical computation of matrix norms, conditioning, scaling
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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