A priori error estimate of stochastic Galerkin method for optimal control problem governed by stochastic elliptic PDE with constrained control

DOI10.1007/s10915-015-0091-7zbMath1342.65150OpenAlexW1893779446MaRDI QIDQ292538

Benxue Gong, Wan-fang Shen, Tong-jun Sun, Wen-bin Liu

Publication date: 8 June 2016

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-015-0091-7

zbMATH Keywords

numerical exampleoptimal control problemspectral methoda priori error estimatesdeterministic constrained controlstochastic elliptic PDEstochastic Galerkin method

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Existence theories for optimal control problems involving partial differential equations (49J20) Discrete approximations in optimal control (49M25)

Related Items

An adaptive hp-version stochastic Galerkin method for constrained optimal control problem governed by random reaction diffusion equations ⋮ A sparse grid stochastic collocation upwind finite volume element method for the constrained optimal control problem governed by random convection diffusion equations ⋮ Stochastic collocation for optimal control problems with stochastic PDE constraints by meshless techniques ⋮ Stochastic perturbation method for optimal control problem governed by parabolic PDEs with small uncertainties ⋮ On spectral Petrov-Galerkin method for solving optimal control problem governed by fractional diffusion equations with fractional noise ⋮ Sample average approximations of strongly convex stochastic programs in Hilbert spaces ⋮ Stochastic discontinuous Galerkin methods for robust deterministic control of convection-diffusion equations with uncertain coefficients ⋮ A Sparse Grid Stochastic Collocation Discontinuous Galerkin Method for Constrained Optimal Control Problem Governed by Random Convection Dominated Diffusion Equations ⋮ Stochastic Galerkin method for optimal control problem governed by random elliptic PDE with state constraints ⋮ A priori error estimate of perturbation method for optimal control problem governed by elliptic PDEs with small uncertainties

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Optimal control with stochastic PDE constraints and uncertain controls
• Convergence rates of best \(N\)-term Galerkin approximations for a class of elliptic SPDEs
• Finite element approximations of stochastic optimal control problems constrained by stochastic elliptic PDEs
• The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications
• An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations
• Robust and efficient methods for stochastic finite element analysis using Monte Carlo simulation
• Sparse finite elements for elliptic problems with stochastic loading
• Inelastic deformation processes with random parameters -- methods of analysis and design.
• On solving elliptic stochastic partial differential equations
• Ingredients for a general purpose stochastic finite elements implementation
• Optimal control of the convection-diffusion equation using stabilized finite element methods
• A Posteriori Error Estimates for Convex Boundary Control Problems
• ERROR ESTIMATES IN THE APPROXIMATION OF OPTIMIZATION PROBLEMS GOVERNED BY NONLINEAR OPERATORS
• Stochastic Spectral Galerkin and Collocation Methods for PDEs with Random Coefficients: A Numerical Comparison
• SOLVING STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS BASED ON THE EXPERIMENTAL DATA
• Parallel Solution of Stochastic PDEs
• Error Estimates of Stochastic Optimal Neumann Boundary Control Problems
• Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients
• A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
• An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
• Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations
• The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
• Finite Element Approximations of an Optimal Control Problem with Integral State Constraint
• High-Order Collocation Methods for Differential Equations with Random Inputs
• A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
• Stochastic differential equations. An introduction with applications.
• Solution of stochastic partial differential equations using Galerkin finite element techniques