Error analysis of finite element approximations of the optimal control problem for stochastic Stokes equations with additive white noise

DOI10.1016/j.apnum.2018.03.002zbMath1397.65255OpenAlexW2789921452WikidataQ130162762 ScholiaQ130162762MaRDI QIDQ1669864

Youngmi Choi, Hyung-Chun Lee

Publication date: 4 September 2018

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2018.03.002

zbMATH Keywords

optimal controlwhite noisestochastic Stokes equationsBRR theory

Mathematics Subject Classification ID

Stokes and related (Oseen, etc.) flows (76D07) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Navier-Stokes equations (35Q30) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) PDEs in connection with control and optimization (35Q93)

Related Items

A stochastic collocation method based on sparse grids for a stochastic Stokes-Darcy model ⋮ Numerical analysis of a Neumann boundary control problem with a stochastic parabolic equation ⋮ A virtual element method for stochastic Stokes equations

Uses Software

• FreeFem++
• NAPACK

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Multilevel and weighted reduced basis method for stochastic optimal control problems constrained by Stokes equations
• Finite element approximations of stochastic optimal control problems constrained by stochastic elliptic PDEs
• The stochastic finite element method: past, present and future
• Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation
• Finite element methods for semilinear elliptic stochastic partial differential equations
• On some control problems in fluid mechanics
• Finite dimensional approximation of nonlinear problems. I: Branches of nonsingular solutions
• On solving elliptic stochastic partial differential equations
• Comparison of approaches for random PDE optimization problems based on different matching functionals
• A least-squares/penalty method for distributed optimal control problems for Stokes equations
• Finite Element Methods for Navier-Stokes Equations
• Analysis and Approximation of the Velocity Tracking Problem for Navier--Stokes Flows with Distributed Control
• Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations
• Finite-Dimensional Approximation of a Class of Constrained Nonlinear Optimal Control Problems
• New development in freefem++
• A finite element approximation of linear stochastic PDEs driven by multiplicative white noise
• ANALYSIS AND COMPUTATIONS OF LEAST-SQUARES METHOD FOR OPTIMAL CONTROL PROBLEMS FOR THE STOKES EQUATIONS