Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Finite-Dimensional Approximation of a Class of Constrained Nonlinear Optimal Control Problems
SIAM Journal on Control and Optimization
Stochastic partial differential equations: a modeling, white noise functional approach
Stochastic partial differential equations: a modeling, white noise functional approach
SIAM Journal on Control and Optimization
Control of the Stochastic Burgers Model of Turbulence
SIAM Journal on Control and Optimization
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
SIAM Journal on Numerical Analysis
A finite element approximation of linear stochastic PDEs driven by multiplicative white noise
International Journal of Computer Mathematics - Recent Advances in Computational and Applied Mathematics in Science and Engineering
Approximating Infinity-Dimensional Stochastic Darcy's Equations without Uniform Ellipticity
SIAM Journal on Numerical Analysis
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We study mathematically and computationally optimal control problems for stochastic partial differential equations with Neumann boundary conditions. The control objective is to minimize the expectation of a cost functional, and the control is of the deterministic, boundary-value type. Mathematically, we prove the existence of an optimal solution and of a Lagrange multiplier; we represent the input data in terms of their Karhunen-Loève expansions and deduce the deterministic optimality system of equations. Computationally, we approximate the finite element solution of the optimality system and estimate its error through the discretizations with respect to both spatial and random parameter spaces.