随机Navier-Stokes方程的多层网格有限元方法研究  

MULTIGRID FINITE ELEMENT METHOD FOR STOCHASTIC NAVIER-STOKES EQUATIONS

作　　者：李峻屹[1] 刘倩[2] 高欣悦 李剑 Li Junyi;Liu Qian;Gao Xinyue;Li Jian(Experimental Training Center,Shaanxi Police Oficer Vocational College,Xi'an 710021;School of Mathematics and Data Science,Shaanxi University of Science and Technology,Xi'an 710021)

机构地区：[1]陕西警官职业学院实验实训中心,西安710021 [2]陕西科技大学数学与数据科学学院,西安710021

出　　处：《高等学校计算数学学报》2023年第3期218-232,共15页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金(11771259);陕西省人工智能联合实验室(2022JC-SYS-05);陕西省教育厅创新团队项目(21JP013);陕西省自然科学基础研究计划重点项目(2023-JC-ZD-02);国家高端外专引进计划项目(G2023041032L)2023。

摘　　要：1引言近年来,随机偏微分问题的应用越来越广泛.科学家们在随机问题方面截至目前已有很多研究[13,16,17,20,21,23,24,28,29].其中文献[13]中提出的Chorin型时间分解方法,证明了速度近似与正弦噪声的强收敛性.对于伴随正弦噪声的随机二维Navier-Stokes(N-S)方程,Carelli和Prohl在文献[16]中证明了隐式和半隐式时间离散格式的速度近似强收敛性.文献[17]中提及到的迭代拆分方法。In this paper,stochastic Navier-Stokes equations with multiplicative noise are studied.This problem is solved by the traditional finite element method,so the multi-grid finite element method is used to solve the stochastic Navier-Stokes problem.This method refers to solving nonlinear stochastic Navier-Stokes problems on the thickest mesh,followed by solving linearstochastic Stokes problems on each fine-grained mesh.Error analysis shows that the multi-grid finite element method provides the same accuracy as the standard mixed finite element method for solving stochastic Navier-Stokes problems,and can save a lot of calculation time.Finally,numerical calculation verifies the effectiveness and efficiency of the theory.

关 键 词：强收敛性 随机问题 分解方法 时间离散格式 拆分方法 有限元方法 偏微分 半隐式 

分 类 号：O241.82[理学—计算数学] O211.63[理学—数学]