A BDDC Preconditioner for the Rotated Q1 FEM for Elliptic Problems with Discontinuous Coefficients

Abstract

We propose a BDDC preconditioner for the rotated $Q_{\mathrm{1}}$ 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.