A conforming enriched finite element method for Stokes interface problems

Hua Wang, Jinru Chen, Pengtao Sun, Nan Wang

Abstract: A new conforming enriched finite element method is presented for Stokes interface problems with interface-unfitted meshes. The conforming enriched finite element pair is constructed based on the MINI element pair. A ghost penalty term is used in the standard discretization form as a stabilization term. An inf–sup stability result is derived, which is uniform with respect to the mesh size. Our method does not limit the viscosity coefficient to be a piecewise constant. Finite element errors are proved to be optimal. Numerical experiments are carried out to validate theoretical results.