高次有限元格式数值求解Stokes方程  

High-order Finite Element Scheme for Numerical Solution of Stokes Equations

作　　者：丁晓 陈璐[1] 江山[1] DING Xiao;CHEN Lu;JIANG Shan(School of Science,Nantong University,Nantong 226019,China)

机构地区：[1]南通大学理学院,江苏南通226019

出　　处：《南通职业大学学报》2023年第3期58-62,共5页Journal of Nantong Vocational University

基　　金：国家自然科学基金面上项目(11771224);2021年度南通市第一批市级科技计划项目(JC2021123)。

摘　　要：为提高二维矢量型Stokes方程的求解精度和收敛阶,应用有限元法进行数值模拟。基于变分虚功原理,构造Lagrange型二次元基函数以形成有限元空间,针对流速的矢量分量形成相应的代数方程组并求解。图像模拟和数值结果均验证,高次有限元解真实有效地逼近了Stokes方程的精确解,且在不同范数度量下,高次有限元格式数值求解方法的精度和收敛阶均达预期。To improve the accuracy and convergence order of two-dimensional vector-type Stokes equations,the finite element method is applied to numerical simulation.Based on the principle of variation virtual work,the Lagrange quadratic basis functions are built to create the finite element space.For vector components of flow velocity,the corresponding algebraic equations are formulated and solved.Both image simulations and numerical results show that the high-order finite element solution truly and effectively approximates the exact solution of the Stokes equation,and the accuracy and convergence order of high-order finite element method for the numerical solution come up to the expectation in different norm metrics.

关 键 词：STOKES方程 有限元法 二次元 数值逼近 

分 类 号：O241.82[理学—计算数学]