Mixed Nitsche extended finite element method for solving three-dimensional H(curl)-elliptic interface problems

Abstract

In this paper, we introduce a Lagrange multiplier to relax the divergence-free constraint and propose a mixed Nitsche extended finite element method for solving three-dimensional H(curl)-elliptic interface problems. To ensure stability, we incorporate ghost penalty terms. By exploiting the commuting relationship of the de Rham complex, we derive an inf-sup stability result for the discrete bilinear form, which is uniform with respect to the mesh size, discontinuous parameters, and the interface position. Based on this, we establish the well-posedness of our method and demonstrate optimal error bounds in the discrete energy norm and $L^2$ norm. Finally, numerical experiments are presented to illustrate the theoretical results.