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Neumann-Neumann algorithms for a mortar Crouzeix-Raviart element for 2nd order elliptic problems. (English) Zbl 1180.65164

This paper proposes two scalable variants of the Neumann-Neumann algorithm for the lowest order Crouzeix-Raviart finite element or the nonconforming \(P_1\) finite element on non matching meshes. The overall discretization is done using a mortar technique which is based on the application of an approximate matching condition for the discrete functions, requiring function values only at the mesh interface nodes. The algorithms are analyzed using the abstract Schwarz framework, proving a convergence which is independent of the jumps in the coefficients of the problem and only depends logarithmically on the ratio between the subdomain size and the mesh size.

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
35J25 Boundary value problems for second-order elliptic equations
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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