Numerical analysis of a characteristic stabilized finite element method for the time-dependent Navier-Stokes equations with nonlinear slip boundary conditions

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:320

Article

Jing, Feifei¹  Li, Jian^2,3  Chen, Zhangxin^1,4  Zhang, Zhonghua⁵ 

[1] Xi An Jiao Tong Univ, Ctr Computat Geosci, Coll Math & Stat, Xian 710049, Peoples R China

[2] Shaanxi Univ Sci & Technol, Dept Math, Sch Arts & Sci, Xian 710021, Peoples R China

[3] Baoji Univ Arts & Sci, Inst Computat Math & Its Applicat, Baoji 721013, Peoples R China

[4] Univ Calgary, Schulich Sch Engn, Dept Chem & Petr Engn, 2500 Univ Dr NW, Calgary, AB T2N 1N4, Canada

[5] Xian Univ Sci & Technol, Sch Sci, Xian 710054, Peoples R China

关键词: Time-dependent Navier-Stokes equations;    Nonlinear slip boundary conditions;    Characteristic method;    Lower order finite element pairs;    Error estimates;   

DOI  :  10.1016/j.cam.2017.01.012

来源: Elsevier

【 摘 要 】

Based on a characteristic method, this work is concerned with a finite element approximation to the time-dependent Navier-Stokes equations with nonlinear slip boundary conditions. Since this slip boundary condition of friction type contains a subdifferential property, its continuous variational problem is formulated as an inequality, which can turn into an equality problem by using a powerful regularized method. Then a fully discrete characteristic scheme under the stabilized lower order finite element pairs is proposed for the equality problem. Optimal error estimates for velocity and pressure are derived under the corresponding L-2, H-1 -norms. Finally, a smooth problem test is reported to demonstrate the theoretically predicted convergence order and the expected slip phenomena, and the simulation of a bifurcated blood flow model is displayed to illustrate the efficiency of the proposed method. (c) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

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