南通大学学报（自然科学版）2024，Vol.23Issue(3)：82-88,7.DOI:10.12194/j.ntu.20230711002
非定常Stokes方程的混合有限元法的高精度逼近
High-precision approximation of mixed finite element method for unsteady Stokes equation
摘要
Abstract
For the two-dimensional unsteady Stokes equations,the Taylor-Hood mixed finite element method is employed for numerical simulation.Firstly,the equation is transformed into the variational form by using the variational principle.Secondly,the domain is uniformly divided into finite triangular elements,and the connection is built among the logical elements and the isoparametric ones.The quadratic basis function is selected for velocity u,and the linear basis function is selected for pressure p,so it establishes a finite element space in spatial scale.Then it is further combined with the finite difference method in temporal scale to construct a fully discrete-type implicit scheme,for selecting the Crank-Nicolson six-point symmetric finite difference scheme is applied.Finally,the equation is transformed into ordinary differential equations for solving its numerical solution,through the numerical example we testify the feasibility and effectiveness of our method.Theoretical constructions and numerical results both validate that the unsteady problem under the space and time discretization it obtains consistent convergent results,which are processed with the linear finite element and the quadratic finite element.And the results of quadratic finite element are much accurate and faster convergence.In order to present the experimental results more intuitively and vividly,this study ends up with several three-dimensional error figures between the exact solution and the finite element solution.关键词
二维非定常Stokes方程/混合有限元法/有限差分格式/一致收敛Key words
two-dimensional unsteady Stokes equation/mixed finite element method/finite difference scheme/consistent convergence分类
数理科学引用本文复制引用
丁晓,陈璐,江山..非定常Stokes方程的混合有限元法的高精度逼近[J].南通大学学报（自然科学版）,2024,23(3):82-88,7.基金项目
国家自然科学基金面上项目(11771224) （11771224）
南通市基础科学研究指令性项目(JC2021123) （JC2021123）
