Two-Level Defect-Correction Method for Steady Navier-Stokes Problem with Friction Boundary Conditions

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.

Author Details

An Liu

Yuan Li

Rong An

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