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Numerical Methods for PDEs: In Occasion of Raytcho Lazarov's 70th Birthday

Ivan Yotov, University of Pittsburgh
Multiscale Domain Decomposition Methods for Porous Media Flow Coupled with Geomechanics


We consider numerical modeling of the system of poroelasticity, which describes fluid flow in deformable porous media. The focus is on locally mass conservative flow discretizations that provide efficient and accurate multiscale approximations on rough grids and for highly heterogeneous media. We employ a multiscale mortar finite element method, where the equations in the coarse elements (or subdomains) are discretized on a fine grid scale, while continuity of normal velocity and stress between coarse elements is imposed via a mortar finite element space on a coarse grid scale. With an appropriate choice of polynomial degree of the mortar space, optimal order convergence is obtained for the method on the fine scale. The algebraic system is reduced via a non-overlapping domain decomposition to a coarse scale mortar interface problem that is solved efficiently using a multiscale flux basis.