Residual-based a posteriori error estimation for multipoint flux mixed finite element methods

摘要

A novel residual-type {it a posteriori} error analysis technique isdeveloped for multipoint flux mixed finite element methods for flow in porousmedia in two or three space dimensions. The derived {it a posteriori} errorestimator for the velocity and pressure error in $L^{2}-$norm consists ofdiscretization and quadrature indicators, and is shown to be reliable andefficient. The main tools of analysis are a locally postprocessed approximationto the pressure solution of an auxiliary problem and a quadrature errorestimate. Numerical experiments are presented to illustrate the competitivebehavior of the estimator.