Ritz–Galerkin Approximation of the Time Optimal Boundary Control Problem for Parabolic Systems with Dirichlet Boundary Conditions

This paper deals with Ritz–Galerkin approximations of the following two problems: (i) boundary-value problems with L₂-boundary data given in the form of Dirichlet boundary conditions; (ii) time optimal control problems for parabolic systems with control acting on the boundary. In both cases, optimal rates of convergence of approximation are obtained. Also, the specialization is considered to approximating with nonconformal elements which are not required to satisfy boundary conditions. Corresponding rates of convergence are also proved.