## A FETI-DP method for Crouzeix-Raviart finite element discretizations.(English)Zbl 1284.65182

Summary: This paper is concerned with the construction and analysis of a parallel preconditioner for a FETI-DP system of equations arising from the nonconforming Crouzeix-Raviart finite element discretization of a model elliptic problem of second order with discontinuous coefficients. We show that the condition number of the preconditioned problem is independent of the coefficient jumps, and grows only as $$(1 + \log(H/h))^2$$, where $$H$$ and $$h$$ are mesh parameters, in other words the preconditioner is quasi optimal.

### 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 65F08 Preconditioners for iterative methods
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