2019/05/08 by Xiaobing Feng, Feng, Xiaobing, Hailong Qiu +1 · 4 citations
Computer Science · Decision Sciences · Economics, Econometrics and Finance · Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Probabilistic and Robust Engineering Design #Stochastic processes and financial applications #cs.NA #math.NA
paper · pdf · doi:10.48550/arxiv.1905.03289
34 pages, 20 figures
arxiv created 2020/04/27 · arxiv updated 2020/04/28
This paper is concerned with fully discrete mixed finite element approximations of the time-dependent stochastic Stokes equations with multiplicative noise. A prototypical method, which comprises of the Euler-Maruyama scheme for time discretization and the Taylor-Hood mixed element for spatial discretization is studied in detail. Strong convergence with rates is established not only for the velocity approximation but also for the pressure approximation (in a time-averaged fashion). A stochastic inf-sup condition is established and used in a nonstandard way to obtain the error estimate for the pressure approximation in the time-averaged fashion. Numerical results are also provided to validate the theoretical results and to gauge the performance of the proposed fully discrete mixed finite methods.