Mixed Finite Element Methods on Nonmatching Multiblock Grids

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Abstract
We consider mixed finite element methods for second order elliptic equations on nonmatching multiblock grids. A mortar finite element space is introduced on the nonmatching 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.

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