A BDDC preconditioner for the rotated $$Q_1$$ FEM for elliptic problems with discontinuous coefficients.(English)Zbl 1406.65114

Summary: We propose a BDDC preconditioner for the rotated $$Q_1$$ finite element method for second order elliptic equations with piecewise but discontinuous coefficients. In the framework of the standard additive Schwarz methods, we describe this method by a complete variational form. We show that our method has a quasioptimal convergence behavior; that is, the condition number of the preconditioned problem is independent of the jumps of the coefficients and depends only logarithmically on the ratio between the subdomain size and the mesh size. Numerical experiments are presented to confirm our theoretical analysis.

MSC:

 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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