(untitled) (Communications in Computational Physics, 2020)
In this paper, a conforming enriched finite element method over an interface-unfitted mesh is developed and analyzed for a type of Stokes-elliptic interface problem with jump coefficients. An inf-sup stability result that is uniform with respect to the mesh size is proved in order to derive the corresponding well-posedness and optimal convergence properties in spite of the low regularity of the problem. The developed new finite element method breaks the limit of the classical immersed finite element method (IFEM) which can only deal with the case of identical governing equations on either side of the interface. Numerical experiments are carried out to validate the theoretical results. This is the first step of our new method to solve complex interface problems with different governing equations on either side of the interface, and will be extended to solve transient interface problems towards fluid-structure interaction problems in the future.