Numerical Experiments for the Arnold-Winther Mixed Finite Elements for the Stokes Problem

The stress-velocity formulation of the stationary Stokes problem allows an Arnold--Winther mixed finite element formulation with some superconvergent reconstruction of the velocity. This local postprocessing gives rise to two reliable a posteriori error estimators which recover optimal convergence order for the stress error estimates. The theoretical results are investigated in numerical benchmark examples.

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