Journal
JOURNAL OF SCIENTIFIC COMPUTING
Volume 88, Issue 2, Pages -Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-021-01546-4
Keywords
Stochastic Stokes equations; Multiplicative noise; Wiener process; Ito stochastic integral; Mixed finite element methods; Inf-sup condition; Error estimates
Categories
Funding
- NSF [DMS-1620168, DMS-2012414]
- NSF of China [11701498]
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This paper deals with fully discrete mixed finite element approximations of the time-dependent stochastic Stokes equations with multiplicative noise. Strong convergence rates are established for both velocity and pressure approximations in a time-averaged fashion. A stochastic inf-sup condition is used in a nonstandard way to obtain error estimates for pressure approximation.
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 element methods.
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