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.