Analysis of a Stokes interface problem |
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Authors: | Maxim A Olshanskii Arnold Reusken |
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Institution: | (1) Department of Mechanics and Mathematics, Moscow State University, Moscow, 119899, Russia;(2) Institut für Geometrie und Praktische Mathematik, RWTH-Aachen, D-52056 Aachen, Germany |
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Abstract: | We consider a stationary Stokes problem with a piecewise constant viscosity coefficient. For the variational formulation of
this problem we prove a well-posedness result in which the constants are uniform with respect to the jump in the viscosity
coefficient. We apply a standard discretization with a pair of LBB stable finite element spaces. The main result of the paper
is an infsup result for the discrete problem that is uniform with respect to the jump in the viscosity coefficient. From this
we derive a robust estimate for the discretization error. We prove that the mass matrix with respect to some suitable scalar
product yields a robust preconditioner for the Schur complement. Results of numerical experiments are presented that illustrate
this robustness property.
This author was supported by the German Research Foundation through the guest program of SFB 540 |
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Keywords: | 65N15 65N22 65N30 65F10 |
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