hp submeshing via non-conforming finite element methods

Non-conformity in the hp version can involve incompatibility in both the de grees and the meshes between adjoining subdomains. In this paper, we show h ow the mortar finite element method M0 and two new variants M1, M2 can be u sed 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 multip lier when the method is implemented via a mixed method. Three-dimensional c onsiderations suggest that our methods M1, M2 are easier to generalize to a rbitrary meshes than M0. (C) 2000 Elsevier Science S.A. All rights reserved .