A posteriori error estimates of triangular mixed finite element methods for semilinear optimal control problems. (English) Zbl 1262.49009

Lu, Zuliang; Chen, Yanping

Adv. Appl. Math. Mech. 1, No. 2, 242-256 (2009).

Summary: In this paper, we present an a posteriori error estimates of semilinear quadratic constrained optimal control problems using triangular mixed finite element methods. The state and co-state are approximated by the order \(k\leq 1\) Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant element. We derive a posteriori error estimates for the coupled state and control approximations. A numerical example is presented in confirmation of the theory.

MSC:

49J20	Existence theories for optimal control problems involving partial differential equations
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

Keywords:

semilinear optimal control problems; mixed finite element methods; a posteriori error estimates