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A posteriori error estimates for the mortar mixed finite element method. (English) Zbl 1094.65114
The authors propose several a posteriori error estimators for mortar mixed finite element discretizations of elliptic equations. 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 the deriving an adaptive process for the mortar grids only.

MSC:
65N15 Error bounds for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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