A Fictitious-Domain Method with Distributed Multiplier for the Stokes Problem

This article is devoted to the numerical analysis of a fictitious domain method for the Stokes problem, where the boundary condition is enforced weakly by means of a multiplier defined in a portion of the domain. In practice, this is applied for example to the sedimentation of many particles in a fluid. It is found that the multiplier is divergence-free. We present here sufficient conditions on the relative mesh sizes for convergence of the discrete method. Also, we show how the constraint on the divergence of the discrete multiplier can be relaxed when such a sedimentation problem is discretized.