RITZ-GALERKIN APPROXIMATION OF THE TIME OPTIMAL BOUNDARY CONTROL PROBLEM FOR PARABOLIC SYSTEMS WITH DIRICHLET BOUNDARY CONDITIONS.
Ritz-Galerkin approximations of the following two problems are considered: (i) boundary-value problems with L//2-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.
SIAM Journal on Control and Optimization
Lasiecka, I. (1984). RITZ-GALERKIN APPROXIMATION OF THE TIME OPTIMAL BOUNDARY CONTROL PROBLEM FOR PARABOLIC SYSTEMS WITH DIRICHLET BOUNDARY CONDITIONS.. SIAM Journal on Control and Optimization, 22 (3), 477-500. https://doi.org/10.1137/0322029