A DPG method for linear quadratic optimal control problems
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Date
2024
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier Ltd
Abstract
The DPG method with optimal test functions for solving linear quadratic optimal control problems with control constraints is studied. We prove existence of a unique optimal solution of the nonlinear discrete problem and characterize it through first-order optimality conditions. Furthermore, we systematically develop a priori as well as a posteriori error estimates. Our proposed method can be applied to a wide range of constrained optimal control problems subject to, e.g., scalar second-order PDEs and the Stokes equations. Numerical experiments that illustrate our theoretical findings are presented.
Description
Keywords
Convergence, Discontinuous Petrov–Galerkin method, Error estimates, Finite elements, Optimal control, Optimal test functions