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Superconvergence Error Estimate of the Bilinear-Constant Scheme for the Stokes Equations with Damping

Superconvergence Error Estimate of the Bilinear-Constant Scheme for the Stokes Equations with Damping

Year:    2024

Author:    Huaijun Yang, Lele Wang, Xin Liao

Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 6 : pp. 1502–1518

Abstract

In this paper, the superconvergence error estimate of a low-order conforming mixed finite element scheme, which is called bilinear-constant scheme, for the Stokes equations with damping is established. In terms of the integral identity technique and dealing with the damping term carefully, the superclose estimates between the interpolation of the exact solution and the finite element solution for the velocity in $H^1$-norm and the pressure in $L^2$-norm are first derived. Then, the global superconvergence results for the velocity in $H^1$-norm and the pressure in $L^2$-norm are derived by a simple postprocessing technique with an economical workload. Finally, some numerical results are presented to demonstrate the correctness of the theoretical analysis.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2022-0182

Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 6 : pp. 1502–1518

Published online:    2024-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    Stokes equations with damping bilinear-constant scheme superclose and superconvergence estimates.

Author Details

Huaijun Yang

Lele Wang

Xin Liao