ERROR ESTIMATES OF STOCHASTIC OPTIMAL NEUMANN BOUNDARY CONTROL PROBLEMS

• Published in: SIAM journal on numerical analysis Vol. 49; no. 3/4; pp. 1532 - 1552
• Main Authors: GUNZBURGER, MAX D., LEE, HYUNG-CHUN, LEE, JANGWOON
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2011
• Subjects: Applied mathematics; Approximation; Boundary conditions; Calculus of variations and optimal control; Control theory; Covariance; Determinism; Error rates; Estimates; Exact sciences and technology; Finite element method; Lagrange multiplier; Lagrange multipliers; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Optimal control; Optimal solutions; Partial differential equations; Partial differential equations, initial value problems and time-dependant initial-boundary value problems; Random variables; Sciences and techniques of general use; 65N15; Error estimation; Differential equation; Existence of solution; Boundary condition; Optimal estimation; Partial differential equation; Non linear equation; Finite element method; Lagrange multiplier; 65K10; Integral equation; 65N30; Stochastic equation; stochastic optimal control; Transcendental equation; Neumann problem; Initial value problem; Discretization method; Equation system; 65C20; Numerical analysis; Boundary value problem; Optimal control; Algebraic equation; Karhunen-Loeve expansion

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...