Title:         Interior superconvergence in mortar and non-mortar 
               mixed finite element methods on non-matching grids

Authors:       G. Pencheva and I. Yotov

Source:        Comp. Meth. in Appl. Mech. and Engng.,
               http://dx.doi.org/10.1016/j.cma.2008.05.010


Abstarct: We establish interior velocity superconvergence estimates
for mixed finite element approximations of second order elliptic
problems on non-matching rectangular and quadrilateral grids.  Both
mortar and non-mortar methods for imposing the interface conditions
are considered. In both cases it is shown that a discrete $L^2$-error
in the velocity in a compactly contained subdomain away from the
interfaces converges of order $O(h^{1/2})$ higher than the error in
the whole domain. For the non-mortar method we also establish pressure
superconvergence, which is needed in the velocity analysis. Numerical
results are presented in confirmation of the theory.