Analysis of a Stokes interface problem

Authors:
Maxim A. Olshanskii;Arnold Reusken
Affiliations:
Department of Mechanics and Mathematics, Moscow State University, 119899, Moscow, Russia;Institut für Geometrie und Praktische Mathematik, RWTH-Aachen, D-52056, Aachen, Germany
Venue:
Numerische Mathematik
Year:
2006

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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.