A reduced-order method for simulation and control of fluid flows
Journal of Computational Physics
Adaptive Finite Element Methods for Optimal Control of Partial Differential Equations: Basic Concept
SIAM Journal on Control and Optimization
Galerkin Proper Orthogonal Decomposition Methods for a General Equation in Fluid Dynamics
SIAM Journal on Numerical Analysis
Perspectives in Flow Control and Optimization
Perspectives in Flow Control and Optimization
"Natural norm" a posteriori error estimators for reduced basis approximations
Journal of Computational Physics - Special issue: Uncertainty quantification in simulation science
Adaptive Space-Time Finite Element Methods for Parabolic Optimization Problems
SIAM Journal on Control and Optimization
Numerical Sensitivity Analysis for the Quantity of Interest in PDE-Constrained Optimization
SIAM Journal on Scientific Computing
Adaptive Finite Elements for Elliptic Optimization Problems with Control Constraints
SIAM Journal on Control and Optimization
Computational Optimization and Applications - Special issue: Numerical analysis of optimization in partial differential equations
Numerical Approximation of Partial Differential Equations
Numerical Approximation of Partial Differential Equations
POD a-posteriori error estimates for linear-quadratic optimal control problems
Computational Optimization and Applications
A Posteriori Error Analysis of the Reduced Basis Method for Nonaffine Parametrized Nonlinear PDEs
SIAM Journal on Numerical Analysis
Proper orthogonal decomposition for reduced basis feedback controllers for parabolic equations
Mathematical and Computer Modelling: An International Journal
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We propose the reduced basis method for the solution of parametrized optimal control problems described by parabolic partial differential equations in the unconstrained case. The method, which is based on an off-line-on-line decomposition procedure, allows at the on-line step large computational cost savings with respect to the “truth” approximation used for defining the reduced basis. An a posteriori error estimate is provided by means of the goal-oriented analysis, thus associating an error bound to each optimal solution of the parametrized optimal control problem and answering to the demand for a reliable method. An adaptive procedure, led by the a posteriori error estimate, is considered for the generation of the reduced basis space, which is set according to the optimal primal and dual solutions of the optimal control problem at hand.