Title:         A posteriori error estimates for the mortar mixed finite element method

Authors:       Mary F. Wheeler and Ivan Yotov

Source:        SIAM J. Numer. Anal. vol. 43 no. 3 (2005) 1021-1042

Status:        Published

Abstarct: Several a posteriori error estimators for mortar mixed
finite element discretizations of elliptic equations are derived. A
residual-based estimator provides optimal upper and lower bounds for
the pressure error. An efficient and reliable estimator for the
velocity and mortar pressure error is also derived, which is based on
solving local (element) problems in a higher-order space. The
interface flux-jump term that appears in the estimators can be used as
an indicator for driving an adaptive process for the mortar grids
only.