A penalty-free .Ñ..(.....)-type immersed FEM for quasi-static electromagnetic interface problems with non-homogeneous jumps

Electromagnetic interface problems commonly arise in numerous physical and engineering applications. Existing unfitted mesh methods frequently encounter suboptimal convergence due to the low solution regularity and the introduction of penalty terms. In this work, we consider a 2D quasi-static electromagnetic model and propose a penalty-free H (∇ ×)-type immersed finite element (IFE) method on unfitted meshes. The Nédélec-type immersed elements are used within a Petrov-Galerkin scheme without any penalties. In order to deal with the non-homogeneous jumps caused by surface charge density and current density, we design special enrichment functions that are directly incorporated into the IFE solutions without any additional degrees of freedom. Hence, the enriched IFE method maintains the same system matrix as the homogeneous case, resulting in better matrix properties. We rigorously establish optimal approximation properties of the enriched IFE space, along with optimal solution error estimates. Numerical experiments are provided to illustrate the accuracy and effectiveness of the proposed method.