TY - JOUR
T1 - Mean-Square Approximation of Navier-Stokes Equations with Additive Noise in Vorticity-Velocity Formulation
AU - Milstein , G.N.
AU - Tretyakov , M.V.
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 1
EP - 30
PY - 2020
DA - 2020/10
SN - 14
DO - http://doi.org/10.4208/nmtma.OA-2020-0034
UR - https://global-sci.org/intro/article_detail/nmtma/18325.html
KW - Navier-Stokes equations, vorticity, numerical method, stochastic partial differential equations, mean-square convergence.
AB - <p style="text-align: justify;">We consider a time discretization of incompressible Navier-Stokes equations with spatial periodic boundary conditions and additive noise in the vorticity-velocity formulation. The approximation is based on freezing the velocity on time
subintervals resulting in a linear stochastic parabolic equation for vorticity. At each
time step, the velocity is expressed via vorticity using a formula corresponding to
the Biot-Savart-type law. We prove the first mean-square convergence order of the
vorticity approximation.</p>