Finite-element-based discretizations of the incompressible Navier-Stokes equations with multiplicative random forcing

作者：Brzezniak Zdzislaw; Carelli Erich; Prohl Andreas^*

来源：IMA Journal of Numerical Analysis, 2013, 33(3): 771-824.

DOI：10.1093/imanum/drs032

• Stochastic Navier-Stokes
• finite elements
• implicit Euler method
• non-Lipschitz drift
• multiplicative noise approximation of martingale solutions

We study finite-element-based space-time discretizations of the incompressible Navier-Stokes equations with noise. In three dimensions, sequences of numerical solutions construct weak martingale solutions for vanishing discretization parameters. In the two-dimensional case, numerical solutions converge to the unique strong solution.

• 出版日期2013-7