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

Part of: Basic methods in fluid mechanics Partial 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)
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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 H1 norm and the pressure in the L2 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 methods 76M10: Finite element methods
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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