An Immersed Raviart–Thomas Mixed Finite Element Method for Elliptic Interface Problems on Unfitted Meshes

This paper presents a lowest-order immersed Raviart–Thomas mixed triangular finite element method for solving elliptic interface problems on unfitted meshes independent of the interface. In order to achieve optimal convergence rates meshes, an (IFE) is constructed by modifying traditional element. Some important properties are derived including unisolvence IFE basis functions, approximation capabilities space and corresponding commuting digram. Optimal error estimates proved rigorously with constant location relative mesh. numerical examples provided validate theoretical analysis.