Convergence rates for an optimally controlled ginzburg-landau equation
2008 (English)Article in journal (Other academic) Submitted
An optimal control problem related to the probability oftransition between stable states for a thermally driven Ginzburg-Landauequation is considered. The value function for the optimal control problemwith a spatial discretization is shown to converge quadratically tothe value function for the original problem. This is done by using thatthe value functions solve similar Hamilton-Jacobi equations, the equationfor the original problem being defined on an infinite dimensionalHilbert space. Time discretization is performed using the SymplecticEuler method. Imposing a reasonable condition this method is shownto be convergent of order one in time, with a constant independent ofthe spatial discretization.
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IdentifiersURN: urn:nbn:se:kth:diva-6030OAI: oai:DiVA.org:kth-6030DiVA: diva2:10609
QS 201203152006-07-212006-07-212012-03-15Bibliographically approved