Convergence rates for an optimally controlled Ginzburg-Landau equation

Details Convergence rates for an optimally controlled Ginzburg-Landau equation Convergence rates for an optimally controlled Ginzburg-Landau equation

2008-09-10

arxiv.org/abs/0809.1834v1

Mathematics

Optimization and Control

43 pages, 10 figures

Scientific paper

An optimal control problem related to the probability of transition between stable states for a thermally driven Ginzburg-Landau equation is considered. The value function for the optimal control problem with a spatial discretization is shown to converge quadratically to the value function for the original problem. This is done by using that the value functions solve similar Hamilton-Jacobi equations, the equation for the original problem being defined on an infinite dimensional Hilbert space. Time discretization is performed using the Symplectic Euler method. Imposing a reasonable condition this method is shown to be convergent of order one in time, with a constant independent of the spatial discretization.

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