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2010 FETI and BDD preconditioners for Stokes–Mortar–Darcy Systems
Juan Galvis, Marcus Sarkis
Commun. Appl. Math. Comput. Sci. 5(1): 1-30 (2010). DOI: 10.2140/camcos.2010.5.1

Abstract

We consider the coupling across an interface of a fluid flow and a porous media flow. The differential equations involve Stokes equations in the fluid region, Darcy equations in the porous region, plus a coupling through an interface with Beaver–Joseph–Saffman transmission conditions. The discretization consists of P2/P1 triangular Taylor–Hood finite elements in the fluid region, the lowest order triangular Raviart–Thomas finite elements in the porous region, and the mortar piecewise constant Lagrange multipliers on the interface. We allow for nonmatching meshes across the interface. Due to the small values of the permeability parameter κ of the porous medium, the resulting discrete symmetric saddle point system is very ill conditioned. We design and analyze preconditioners based on the finite element by tearing and interconnecting (FETI) and balancing domain decomposition (BDD) methods and derive a condition number estimate of order C1(1+(1κ)) for the preconditioned operator. In case the fluid discretization is finer than the porous side discretization, we derive a better estimate of order C2((κ+1)(κ+(hp)2)) for the FETI preconditioner. Here hp is the mesh size of the porous side triangulation. The constants C1 and C2 are independent of the permeability κ, the fluid viscosity ν, and the mesh ratio across the interface. Numerical experiments confirm the sharpness of the theoretical estimates.

Citation

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Juan Galvis. Marcus Sarkis. "FETI and BDD preconditioners for Stokes–Mortar–Darcy Systems." Commun. Appl. Math. Comput. Sci. 5 (1) 1 - 30, 2010. https://doi.org/10.2140/camcos.2010.5.1

Information

Received: 22 November 2008; Revised: 17 November 2009; Accepted: 29 November 2009; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1189.35226
MathSciNet: MR2600819
Digital Object Identifier: 10.2140/camcos.2010.5.1

Subjects:
Primary: 35Q30 , 65N22 , 65N30 , 65N55 , 76D07

Keywords: balancing domain decomposition , discontinuous coefficients , FETI , mortar , mortar elements , nonmatching grids , saddle point problems , Stokes–Darcy coupling

Rights: Copyright © 2010 Mathematical Sciences Publishers

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