An hp-Nitsche's method for interface problems with nonconforming unstructured finite element meshes

In this paper we propose an hp-Nitsche's method for the finite element solution of interface elliptic problems using non-matched unstructured meshes of triangles and parallelograms in ℝ2 and tetrahedra and parallelepipeds in ℝ3. We obtain an explicit lower bound for the penalty weighting function in terms of the local inverse inequality constant. We prove a priori error estimates which are explicit in the mesh size h and in the polynomial degree p. The error bound is optimal in h and suboptimal in polynomial degree by p1/2