An additive Schwarz preconditioner for the mortar-type rotated Q1 FEM for elliptic problems with discontinuous coefficients

In this paper, we propose an additive Schwarz preconditioner for the mortar-type rotated Q1 finite element method for second order elliptic partial differential equations with piecewise but discontinuous coefficients. The work here is an extension of the research presented in [L. Marcinkowski, Additive Schwarz method for mortar discretization of elliptic problems with P1 non-conforming elements, BIT 45 (2005) 375–394]. Our analysis is valid for rectangular or L-shaped domains, which are partitioned by rectangular subdomains and meshes. We have shown that our proposed method has a quasi-optimal convergence behavior, i.e., the condition number of the preconditioned problem is O((1+log2(H/h))), which is independent of the jump in the coefficient. Numerical experiments presented in this paper have confirmed our theoretical analysis.