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 mesh-refining algorithms. Numerical experiments confirm our theoretical findings and illustrate the accuracy of the guaranteed upper error bounds even with reduced regularity.

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