Sparse Grid Collocation Method for an Optimal Control Problem Involving a Stochastic Partial Differential Equation with Random Inputs

DOI10.4208/eajam.041013.180314azbMath1309.49025OpenAlexW2317708693WikidataQ115211254 ScholiaQ115211254MaRDI QIDQ5175447

Hyung-Chun Lee, Nary Kim

Publication date: 23 February 2015

Published in: East Asian Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4208/eajam.041013.180314a

zbMATH Keywords

optimal controlstochastic partial differential equationsfinite element methodsdistributed controlsparse grid collocation

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Optimal stochastic control (93E20) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) PDEs with randomness, stochastic partial differential equations (35R60) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55) Discrete approximations in optimal control (49M25) Optimality conditions for problems involving randomness (49K45) Existence of optimal solutions to problems involving randomness (49J55)

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Cites Work

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• Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation
• Finite dimensional approximation of nonlinear problems. I: Branches of nonsingular solutions
• Sparse finite elements for elliptic problems with stochastic loading
• Finite elements for elliptic problems with stochastic coefficients
• On solving elliptic stochastic partial differential equations
• SOLVING STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS BASED ON THE EXPERIMENTAL DATA
• Error Estimates of Stochastic Optimal Neumann Boundary Control Problems
• Optimal control of a stochastic heat equation with boundary-noise and boundary-control
• 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
• Finite Element Methods for Navier-Stokes Equations
• Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations
• High-Order Collocation Methods for Differential Equations with Random Inputs
• Solution of stochastic partial differential equations using Galerkin finite element techniques