A Priori and A Posteriori Analysis of Mixed Finite Element Methods for Nonlinear Elliptic Equations
SIAM Journal on Numerical Analysis
A Stochastic Mortar Mixed Finite Element Method for Flow in Porous Media with Multiple Rock Types
SIAM Journal on Scientific Computing
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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.