Locally Conservative Immersed Finite Element Method for Elliptic Interface Problems

In this paper, we introduce a locally conservative enriched immersed finite element method (EIFEM) to tackle the elliptic problem with interface. The is useful for handling interface mesh unfit However, all currently available under IFEM framework may not be designed consider flux conservation. We provide an efficient and effective remedy issue by introducing local piecewise constant enrichment, which provides flux. have also constructed analyzed auxiliary space preconditioner resulting system based on application of algebraic multigrid method. new observation in work that imposing strong Dirichlet boundary condition standard part EIFEM, are able remove zero eigen-mode EIFEM while still weakly assigned enrichment EIFEM. A couple issues relevant given has been discussed clarified as well. Numerical tests provided confirm theoretical development.