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We develop a mixed finite element domain decomposition method on non-matchinggrids for the Biot system of poroelasticity. A displacement-pressure vectormortar function is introduced on the interfaces and utilized as a Lagrangemultiplier to impose weakly continuity of normal stress and normal velocity.The mortar space can be on a coarse scale, resulting in a multiscaleapproximation. We establish existence, uniqueness, stability, and errorestimates for the semidiscrete continuous-in-time formulation under a suitablecondition on the richness of the mortar space. We further consider afully-discrete method based on the backward Euler time discretization and showthat the solution of the algebraic system at each time step can be reduced tosolving a positive definite interface problem for the composite mortarvariable. A multiscale stress-flux basis is constructed, which makes the numberof subdomain solves independent of the number of iterations required for theinterface problem, as well as the number of time steps. We present numericalexperiments verifying the theoretical results and illustrating the multiscalecapabilities of the method for a heterogeneous benchmark problem.

Multiscale mortar mixed finite element methods for the Biot system of poroelasticity