Premium
Asymptotic preserving time‐discretization of optimal control problems for the Goldstein–Taylor model
Author(s) -
Albi Giacomo,
Herty Michael,
Jörres Christian,
Pareschi Lorenzo
Publication year - 2014
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21877
Subject(s) - mathematics , discretization , optimal control , limiting , taylor series , class (philosophy) , partial differential equation , mathematical optimization , mathematical analysis , computer science , mechanical engineering , artificial intelligence , engineering
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, 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. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1770–1784, 2014