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DOMAIN DECOMPOSITION FOR POROELASTICITY AND ELASTICITY WITH DG JUMPS AND MORTARS

Laboratoire Jacques-Louis Lions, C.N.R.S. and Université Pierre et Marie Curie, 75252 Paris Cedex 05, France

Department of Mathematics, Texas A&M University, College Station, TX 77843, USA

Center for Subsurface Modeling (CSM), Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin, Austin TX 78712, USA

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M. F. WHEELER

Center for Subsurface Modeling (CSM), Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin, Austin TX 78712, USA

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, and

T. WILDEY

Center for Subsurface Modeling (CSM), Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin, Austin TX 78712, USA

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https://doi.org/10.1142/S0218202511005039Cited by:28 (Source: Crossref)

Abstract

We couple a time-dependent poroelastic model in a region with an elastic model in adjacent regions. We discretize each model independently on non-matching grids and we realize a domain decomposition on the interface between the regions by introducing DG jumps and mortars. The unknowns are condensed on the interface, so that at each time step, the computation in each subdomain can be performed in parallel. In addition, by extrapolating the displacement, we present an algorithm where the computations of the pressure and displacement are decoupled. We show that the matrix of the interface problem is positive definite and establish error estimates for this scheme.

Keywords:

AMSC: 35Q86, 65M12, 65M15, 65M60, 74F10

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