An unfitted finite element method, based on Nitsche's method, for elliptic interface problems

Journal article, 2002

In this paper we propose a method for the finite element solution of elliptic interface problems, using an approach due to Nitsche. The method allows for discontinuities, internal to the elements, in the approximation across the interface. We show that the optimal order of convergence holds without restrictions on the location of the interface relative to the mesh. Further, we derive a posteriori error estimates for the purpose of controlling functionals of the error and present some numerical examples.