TY - JOUR
T1 - Auxiliary Equations Approach for the Stochastic Unsteady  Navier-Stokes Equations with Additive Random Noise
AU - Zhao , Wenju
AU - Gunzburger , Max
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 1
EP - 26
PY - 2019
DA - 2019/12
SN - 13
DO - http://doi.org/10.4208/nmtma.OA-2019-0055
UR - https://global-sci.org/intro/article_detail/nmtma/13428.html
KW - Stochastic Navier-Stokes equations,  Martingale regularization method, Galerkin finite element method,  white noise.
AB - <p style="text-align: justify;">This paper presents a Martingale regularization method for the stochastic Navier-Stokes equations with additive noise. The original system is split into two equivalent parts, the linear stochastic Stokes equations with Martingale solution and the stochastic modified Navier-Stokes equations with relatively-higher regularities. Meanwhile, a fractional Laplace operator is introduced to regularize the noise term. The stability and convergence of numerical scheme for the pathwise modified Navier-Stokes equations are proved.&nbsp;The comparisons of non-regularized and regularized noises for the Navier-Stokes system are numerically presented to further demonstrate the efficiency of our numerical scheme.</p>