Mixed Finite Element Methods on Non-Matching Multiblock Grids

Abstract

. We consider mixed finite element methods for second order elliptic equations on non-matching multiblock grids. A mortar finite element space is introduced on the non-matching interfaces. We approximate in this mortar space the trace of the solution, and we impose weakly a continuity of flux condition. A standard mixed finite element method is used within the blocks. Optimal order convergence is shown for both the solution and its flux. Moreover, at certain discrete points, superconvergence is obtained for the solution, and also for the flux in special cases. Computational results using an efficient parallel domain decomposition algorithm are presented in confirmation of the theory. Key words. Mixed finite element, mortar finite element, error estimates, superconvergence, multiblock, non-conforming grids AMS subject classifications. 65N06, 65N12, 65N15, 65N22, 65N30 1. Introduction. Mixed finite element methods have become popular due to their local (mass) conservation property and ..