An optimally convergent higher-order finite element coupling method for interface and domain decomposition problems

Abstract

We present a new, optimally accurate finite element method for interface problems that does not require matching interface grids or spatially coincident interfaces. The key idea is to enforce “extended” interface conditions through pullbacks onto the discretized interfaces. In so doing our approach circumvents the accuracy barriers prompted by polytopial approximations of the subdomains and enables high-order finite element solutions without needing more expensive curvilinear maps. Since the discrete interfaces are not required to match, the approach is also appropriate for multiphysics couplings where each subdomain is meshed independently and solved by a separate code. Error analysis reveals that the new approach is well posed and optimally convergent with respect to a broken H1 norm. Numerical examples confirm this result and also indicate optimal convergence in a broken L2 norm.