hp submeshing via non-conforming finite element methods Original Research Article

Non-conformity in the hp version can involve incompatibility in both the degrees and the meshes between adjoining subdomains. In this paper, we show how the mortar finite element method M0 and two new variants M1, M2 can be used to join together such incompatible hp sub-discretizations. Our results show optimality of the resulting non-conforming method for various h,p and hp discretizations, including the case of exponential hp convergence over geometric meshes. We also present numerical results for the Lagrange multiplier when the method is implemented via a mixed method. Three-dimensional considerations suggest that our methods M1, M2 are easier to generalize to arbitrary meshes than M0.