Distributed Lagrange multiplier/fictitious domain finite element method for Stokes/parabolic interface problems with jump coefficients

摘要

In this paper, the distributed Lagrange multiplier/fictitious domain (DLM/FD)-mixed finite element method is developed and analyzed for a type of linearized fluid-structure interaction problem-the transient Stokes/parabolic interface problem with jump coefficients. Stability and optimal convergence properties are obtained for both semi- and fully discrete mixed finite element scheme. Numerical experiments are carried out to validate the theoretical results. Similar DLM/FD method can be developed to tackle FS1 problems with different compressibility for the fluid and the structure in the future.