2022/11/04 by Liet Vo, Vo, Liet · 3 citations
Earth and Planetary Sciences · Economics, Econometrics and Finance · Engineering · #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Meteorological Phenomena and Simulations #Numerical Analysis (math.NA) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2211.02757
openalex publication_date 2022/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we propose a new approach for the time-discretization of the incompressible stochastic Stokes equations with multiplicative noise. Our new strategy is based on the classical Milstein method from stochastic differential equations. We use the energy method for its error analysis and show a strong convergence order of at most 1 for both velocity and pressure approximations. The proof is based on a new Hölder continuity estimate of the velocity solution. While the errors of the velocity approximation are estimated in the standard L2- and H1-norms, the pressure errors are carefully analyzed in a special norm because of the low regularity of the pressure solution. In addition, a new interpretation of the pressure solution, which is very useful in computation, is also introduced. Numerical experiments are also provided to validate the error estimates and their sharpness.