A Stokes Interface Problem: Stability, Finite Element Analysis and a Robust Solver

We consider a stationary Stokes problem with a piecewise constant viscosity coefficient. For the variational formulation of this problem in H0 × L2 we prove a well-posedness result in which the constants are uniform with respect to the jump in the viscosity coefficient. For a standard discretization with a pair of LBB stable finite element spaces we prove an infsup stability result uniform with respect to the jump in the viscosity coefficient. From this we derive an estimate for the discretization error. We introduce a robust preconditioner for the Schur complement of the discrete system. Results of numerical experiments are presented.