随机Stokes方程的高精度数值逼近  

A High-Order Approximation Scheme for Stochastic Stokes Equations

作　　者：曲东[1] 钟伟[1] 杨晶[2] 

机构地区：[1]九江学院理学院 [2]九江学院会计学院,江西九江332005

出　　处：《九江学院学报（自然科学版）》2010年第1期30-33,共4页Journal of Jiujiang University：Natural Science Edition

摘　　要：本文旨在数值逼近带有随机扩散项的Stokes方程,即方程中的扩散项带有一定程度的不确定性.基于有限维噪音假设,笔者针对该类方程设计算法的有效实现技巧.假设参数的不确定性用具有均匀分布的随机变量来刻画,数值算例成功验证了本文设计的数值方法具有指数阶收敛速度;另外,笔者最后采用传统的蒙特卡罗模拟验证了逼近方法的高精度.In this paper,authors approximated the Stokes equations with random diffusions,i.e.,the uncertainties exist in the diffusion term.Based on the finite dimensional noise assumptions,authors designed an effective algorithm to gain the numerical solutions.By assuming the uncertainty is characterized by the uniform random variables,authors showed the exponential convergence rate of the algorithm by numerical examples.Moreover,authors validated the high accuracy of the numerical solution against by Monte Carlo simulations.

关 键 词：随机Stokes方程 随机扩散 均匀分布 LEGENDRE多项式 

分 类 号：O241.82[理学—计算数学]