An Interface-Unfitted Conforming Enriched Finite Element Method for Stokes-Elliptic Interface Problems with Jump Coefficients (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 problemwith jump coefficients. An inf-sup stability result that is uniform with respect to themesh size is proved in order to derive the corresponding well-posedness and optimalconvergence properties in spite of the low regularity of the problem. The developednew finite element method breaks the limit of the classical immersed finite elementmethod (IFEM) which can only deal with the case of identical governing equationson either side of the interface. Numerical experiments are carried out to validate thetheoretical results. This is the first step of our new method to solve complex interfaceproblems with different governing equations on either side of the interface, and willbe extended to solve transient interface problems towards fluid-structure interactionproblems in the future.
Keywords: Conforming enriched finite element; interface-unfitted mesh; Stokes-elliptic interface problem; inf-sup condition; optimal convergence.