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.