A Priori and A Posteriori Pseudostress-velocity Mixed Finite Element Error Analysis for the Stokes Problem

The pseudostress-velocity formulation of the stationary Stokes problem allows a Raviart-Thomas mixed finite element formulation with quasi-optimal convergence and some superconvergent reconstruction of the velocity. This local postprocessing gives rise to some averaging a posteriori error estimator with explicit constants for reliable error control. Standard residual-based explicit a posteriori error estimation is shown to be reliable and efficient and motivates adaptive meshrefining algorithms. Numerical experiments confirm our theoretical findings and illustrate the accuracy of the guaranteed upper error bounds even with reduced regularity.