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

Part of:Basic methods in fluid mechanicsPartial differential equations, boundary value problems

Published online by Cambridge University Press:  19 September 2016

An Liu,
Yuan Li and
Rong An
An Liu
Affiliation:
College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, China
Yuan Li
Affiliation:
College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, China
Rong An*
Affiliation:
College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, China
*
*Corresponding author. Email:anrong702@gmail.com, anrong702@aliyun.com (R. An)

Abstract

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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.

Keywords

Navier-Stokes equationsfriction boundary conditionsvariational inequality problemsdefect-correction methodtwo-level mesh method

MSC classification

Secondary:65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods76M10: Finite element methods

Information

Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 6 , December 2016, pp. 932 - 952
Copyright
Copyright © Global-Science Press 2016 

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