Two-Level Defect-Correction Method for Steady Navier-Stokes Problem with Friction Boundary Conditions
Year: 2016
Author: An Liu, Yuan Li, Rong An
Advances in Applied Mathematics and Mechanics, Vol. 8 (2016), Iss. 6 : pp. 932–952
Abstract
In this paper, we present two-level defect-correction finite element method for steady Navier-Stokes equations at high Reynolds number with the friction boundary conditions, which results in a variational inequality problem of the second kind. Based on Taylor-Hood element, we solve a variational inequality problem of Navier-Stokes type on the coarse mesh and solve a variational inequality problem of Navier-Stokes type corresponding to Newton linearization on the fine mesh. The error estimates for the velocity in the $H^1$ norm and the pressure in the $L^2$ norm are derived. Finally, the numerical results are provided to confirm our theoretical analysis.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.2014.m595
Advances in Applied Mathematics and Mechanics, Vol. 8 (2016), Iss. 6 : pp. 932–952
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Navier-Stokes equations friction boundary conditions variational inequality problems defect-correction method two-level mesh method.
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