An Efficient Iterative Method for Stokes equations and Lame equations for nearly incompressible media with highly discontinuous coefficients

N. S. Bakhvalov, A. V. Knyazev and R. R. Parashkevov
December 1, 1997
URN = ncstrl.cudenver_ccm/UCD-CCM-120

Abstract: We consider an efficient iterative solution technique for the isotropic linear elasticity (Lam\'{e}) equations for nearly incompressible media and Stokes equations with highly discontinuous coefficients. The iterative method involves a special choice for an initial guess and a preconditioner based on solving a constant coefficient problem. For simplicity, we only analyze a periodic boundary value problem. Some other standard boundary value problems can be treated similarly, or can be reduced to the periodic case by using the fictitious domain method. For the Lam\'{e} equations, we also discuss the case of absolutely compressible media.

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