Superconvergent mixed finite element methods for the pseudostress-velocity formulation of the Oseen equation
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We present a priori and superconvergence error estimates of mixed finite element methods for the pseudostress-velocity formulation of the Oseen equation. In particular, we derive supercloseness estimates on the velocity and a priori error estimates under unstructured grids. We also obtain supercloseness estimates on the pseudostress under certain structured grids. With the help of supercloseness and postprocessing procedures, postprocessed numerical velocity and pseudostress are shown to be superconvergent. We finally present numerical experiments to verify the theoretical results and illustrate the effectiveness of the superconvergent recovery-based a posteriori error estimator.
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