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Superconvergent Pseudostress-Velocity Finite Element Methods for the Oseen Equations

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Abstract

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 superconvergence estimates for the velocity and a priori error estimates under unstructured grids, and obtain superconvergence results for the pseudostress under certain structured grids. A variety of numerical experiments validate the theoretical results and illustrate the effectiveness of the superconvergent recovery-based adaptive mesh refinement. It is also numerically shown that the proposed postprocessing yields apparent superconvergence in a benchmark problem for the incompressible Navier–Stokes equation.

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Data Availability

Data sharing is not applicable to this article as no datasets were generated or analysed during the current study.

Code Availability Statement

The code used in this study is available from the authors upon request.

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  1. Department of Engineering Science and Mechanics, The Pennsylvania State University, University Park, PA, 16802, USA

    Xi Chen

  2. Department of Mathematics, The Pennsylvania State University, University Park, PA, 16802, USA

    Yuwen Li

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Chen, X., Li, Y. Superconvergent Pseudostress-Velocity Finite Element Methods for the Oseen Equations. J Sci Comput 92, 17 (2022). https://doi.org/10.1007/s10915-022-01856-1

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