Finite Element Approximation of Parabolic Time Optimal Control Problems

The numerical approximation of a parabolic time optimal control problem via piecewise linear splines, is considered. At each stage of the approximation a bang-bang approximate control is selected by solving for its switching times as the solution of a constrained nonlinear least squares optimization problem. The well-posedness of the approximation scheme is shown and the rate of convergence to the exact solution investigated. Numerical results for some one- and two-dimensional parabolic control problems are given.