Distributed Lagrange Multiplier-Fictitious Domain Finite Element Method for Stokes Interface Problems

Abstract

In this paper, the distributed Lagrange multiplier-fictitious domain (DLM/FD) finite element method is studied for a type of steady state Stokes interface problems with jump coefficients, and its well-posedness, stability and optimal convergence properties are analyzed by proving an $inf$-$sup$ condition for a nested saddle-point problem that is induced by both Stokes equations and DLM/FD method in regard to Stokes variables (velocity and pressure) and Lagrange multipliers. Numerical experiments validate the obtained convergence theorem of DLM/FD finite element method for Stokes interface problems with respect to different jump ratios.