Robust a posteriori error estimation for mixed finite element approximation of linear poroelasticity

Abstract

Abstract This work is dedicated to the memory of John W. Barrett, who introduced the concept of inf–sup stability to the corresponding author in the bar at the MAFELAP conference in 1981. We analyze a posteriori error estimators for locking-free mixed finite element approximation of Biot’s consolidation model. Three estimators are described. The simplest of these is a conventional residual-based estimator. We establish bounds relating the estimated and true errors, and show that these are independent of the physical parameters. The other two estimators require the solution of local problems. These local problem estimators are also shown to be reliable, efficient and robust. Numerical results are presented that validate the theoretical estimates, and illustrate the effectiveness of the estimators in guiding adaptive solution algorithms. The IFISS and T-IFISS software packages used for the computational experiments are available online.