Error analysis of finite element approximations of the optimal control problem for stochastic Stokes equations with additive white noise. (English) Zbl 1397.65255
Summary: Finite element approximation solutions of the optimal control problems for stochastic Stokes equations with the forcing term perturbed by white noise are considered. To obtain the most efficient deterministic optimal control, we set up the cost functional as we proposed in [H.-C. Lee and M. D. Gunzburger, Comput. Math. Appl. 73, No. 8, 1657–1672 (2017; Zbl 1370.49032)]. Error estimates are established for the fully coupled optimality system using Green’s functions and Brezzi-Rappaz-Raviart theory. Numerical examples are also presented to examine our theoretical results.
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 35R60 | PDEs with randomness, stochastic partial differential equations |
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 35Q93 | PDEs in connection with control and optimization |
| 35Q30 | Navier-Stokes equations |
| 60H35 | Computational methods for stochastic equations (aspects of stochastic analysis) |
| 76D07 | Stokes and related (Oseen, etc.) flows |
Citations:
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