Convergence of finite element approximations to state constrained convex parabolic boundary control problems

This paper is concerned with the numerical solution of state constrained parabolic boundary control problems by finite element approximations. Error estimates for the optimal values, and in the coercive case for the optimal solutions, are derived. These estimates are used to prove convergence results under rather weak assumptions. In the noncoercive case a bang-bang principle is shown to obtain convergence results for the discrete controls also. A discussion of several numerical examples concludes the paper.