Convergence analysis and error estimate of finite element method of a nonlinear fluid-structure interaction problem

被引:1
作者
Zhao, Xin [1 ]
Liu, Xin [2 ]
Li, Jian [3 ]
机构
[1] Baoji Univ Arts & Sci, Dept Geog Sci & Environm Engn, Key Lab Disaster Monitoring & Mech Simulat Shaanx, Baoji 721013, Peoples R China
[2] Northwestern Polytech Univ, Sch Math & Stat, Xian 710129, Peoples R China
[3] Shaanxi Univ Sci & Technol, Sch Arts & Sci, Dept Math, Xian 710021, Peoples R China
来源
AIMS MATHEMATICS | 2020年 / 5卷 / 05期
关键词
fluid-structure interaction; Navier-Stokes equations; finite element method; convergence analysis; error estimate; numerical analysis; NAVIER-STOKES PROBLEM; APPROXIMATION; FORMULATION;
D O I
10.3934/math.2020337
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, a semi-discrete finite element method for the nonlinear fluid-structure interaction problem interacts between the Navier-Stokes fluids and linear elastic solids, is studied and developed. A classical mixed variational principle of the weak formulation is given, and the corresponding finite element method is defined. As for the nonlinearity arising from the nonlinear interaction problem, we consider in time of a solution for suitably small data, and uniqueness hypothesis. This approach is fairly robust and adapts to the important case of interface with fractures or cracks. Convergence and estimate of the finite element method are also obtained for the nonlinear fluid-structure interaction problem. Finally, numerical experiments are presented to show the performance of the proposed method.
引用
收藏
页码:5240 / 5260
页数:21
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