An interface penalty parameter free nonconforming cut finite element method for elliptic interface problems

Abstract

In this paper, we explore a nonconforming cut finite element method based on the nonsymmetric version of Nitsche's method without interface penalty for elliptic interface problems. In contrast to symmetric Nitsche methods, this penalty parameter free scheme does not need “sufficiently large” parameters to ensure the stability. Our main results are that a special function is constructed and the stability of the bilinear form is proved by an inf-sup argument. The optimal convergence in the energy norm and the suboptimal convergence in L2-norm are derived. The suboptimality is due to the lack of adjoint consistency of our formulation. Numerical examples are provided to support the theoretical analysis.