Asymptotic Preserving time-discretization of optimal control problems for the Goldstein-Taylor model

Giacomo Albi, Michael Herty, Christian Jörres, Lorenzo Pareschi
(01/08/2013 Numerical methods for PDEs, 30, 6, pp.1770-1784, 2014arXiv:1307.8303)

We consider the development of implicit-explicit time integration schemes for optimal control problems governed by the Goldstein-Taylor model. In the diffusive scaling this model is a hyperbolic approximation to the heat equation. We investigate the relation of time integration schemes and the formal Chapman-Enskog type limiting procedure.
For the class of stiffly accurate implicit-explicit Runge-Kutta methods (IMEX) the discrete optimality system also provides a stable numerical method for optimal control problems governed by the heat equation. Numerical examples illustrate the expected behavior.