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A Legendre-Galerkin spectral method for optimal control problems governed by elliptic equations. (English) Zbl 1175.49003

Summary: We study the Legendre-Galerkin spectral approximation for a constrained optimal control problem. We first derive a priori error estimates for the spectral approximation of optimal control problems. Then a posteriori error estimates are obtained for both the state and the control approximation. A preconditioning projection algorithm is proposed with some numerical tests.

MSC:

49J20 Existence theories for optimal control problems involving partial differential equations
65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L12 Finite difference and finite volume methods for ordinary differential equations
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