Optimal hp convergence over partitioned domains

Manil Suri
Department of Mathematics and Statistics
University of Maryland, Baltimore County

Abstract: We consider methods for the decomposition and recomposition of a domain into subdomains where no compatibility is assumed between the meshes on the interfaces. Instead, Lagrange multipliers and interface variables are used to weakly enforce continuity. Such non-conforming methods are of interest, for example, when different parts of a problem are to be meshed independently, or when localized mesh refinement capability is desired. If the domain has singularities, then it is essential to use non-quasiuniform refined meshes to get good convergence rates. For many applications, such refinement would also be necessary on the interfaces. We show how optimal h and hp convergence can be achieved in the presence of such non-quasiuniform refined meshes. In particular, we present estimates for the Mortar Finite Element Method that are uniform both in terms of the mesh spacing h and the polynomial degree p, and show that it gives exponential hp convergence.