Error estimates for a galerkin approximation of a parabolic control problem

Summary Numerical approximation of a parabolic control problem with a Neumann boundary condition control is considered. The observation is the final state. The numerical approximation is based on backward discretization with respect to time and a Galerkin method in the space variables. Optimal (except for a logarithmic term) L² error estimates are derived for the optimal state. Certain error estimates for the optimal control are also given. Entrata in Redazione il 4 maggio 1977. This work was supported by the Norwegian Research Council for Science and the Humanities.