论文标题
通过人工压缩性，随机Navier-Stokes方程的数值近似
Numerical approximation of the stochastic Navier-Stokes equations through artificial compressibility
论文作者
论文摘要
通过涉及参数$ε$的伪压缩性技术，提出了不可压缩流体的二维不稳定随机Navier-Stokes方程的建设性数值近似。空间和时间通过有限元近似和EULER方法离散。在本文中研究了建议的数值方案的收敛分析。它基于局部单调性属性，该属性允许在最初引入的概率空间内融合到Navier-Stokes方程的独特强溶液。在参数$ε$上施加了合理的最佳条件，以确保在最佳速度范围内收敛。
A constructive numerical approximation of the two-dimensional unsteady stochastic Navier-Stokes equations of an incompressible fluid is proposed via a pseudo-compressibility technique involving a parameter $ε$. Space and time are discretized through a finite element approximation and an Euler method. The convergence analysis of the suggested numerical scheme is investigated throughout this paper. It is based on a local monotonicity property permitting the convergence toward the unique strong solution of the Navier-Stokes equations to occur within the originally introduced probability space. Justified optimal conditions are imposed on the parameter $ε$ to ensure convergence within the best rate.
