Asymptotic preserving time‐discretization of optimal control problems for the Goldstein–Taylor model
DOI10.1002/num.21877zbMath1311.65079arXiv1307.8303OpenAlexW1552145224MaRDI QIDQ4982254
Michael Herty, Christian Jörres, Giacomo Albi, Lorenzo Pareschi
Publication date: 24 March 2015
Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1307.8303
optimal controlnumerical examplehyperbolic conservation lawskinetic equationsoptimal boundary controlasymptotic-preserving schemesimplicit-explicit Runge-Kutta methodsGoldstein-Taylor modelChapman-Enskog-type limiting procedure
Numerical optimization and variational techniques (65K10) Existence theories for optimal control problems involving partial differential equations (49J20) Discrete approximations in optimal control (49M25)
Related Items
Cites Work
- Unnamed Item
- Numerical schemes for kinetic equations in diffusive regimes
- Adjoint IMEX-based schemes for control problems governed by hyperbolic conservation laws
- Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation
- Time discretizations for numerical optimisation of hyperbolic problems
- Initial boundary value problems for the Carleman equation
- Automatic differentiation of explicit Runge-Kutta methods for optimal control
- Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
- On the shift differentiability of the flow generated by a hyperbolic system of conservation laws
- Runge-Kutta methods in optimal control and the transformed adjoint system
- Additive Runge-Kutta schemes for convection-diffusion-reaction equations
- Numerical schemes for hyperbolic conservation laws with stiff relaxation terms
- W-methods in optimal control
- Computation of order conditions for symplectic partitioned Runge-Kutta schemes with application to optimal control
- Analytic adjoint solutions for the quasi-one-dimensional Euler equations
- Asymptotic Preserving Implicit-Explicit Runge--Kutta Methods for Nonlinear Kinetic Equations
- Implicit-Explicit Runge--Kutta Schemes for Numerical Discretization of Optimal Control Problems
- High-Order Asymptotic-Preserving Methods for Fully Nonlinear Relaxation Problems
- On convergence of a receding horizon method for parabolic boundary control
- Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality
- AN ALTERNATING DESCENT METHOD FOR THE OPTIMAL CONTROL OF THE INVISCID BURGERS EQUATION IN THE PRESENCE OF SHOCKS
- The nonlinear diffusion limit for generalized Carleman models: the initial-boundary value problem
- Order Conditions for Canonical Runge–Kutta Schemes
- Diffusive Relaxation Schemes for Multiscale Discrete-Velocity Kinetic Equations
- Space Localization and Well-Balanced Schemes for Discrete Kinetic Models in Diffusive Regimes
- Numerical Schemes for Hyperbolic Systems of Conservation Laws with Stiff Diffusive Relaxation
- Second-Order Runge--Kutta Approximations in Control Constrained Optimal Control
- The Euler approximation in state constrained optimal control
- The fluid dynamical limit of the Carleman equation with reflecting boundary
- A variational calculus for discontinuous solutions of systems of conservation laws
- Implicit-Explicit Runge--Kutta Schemes for Hyperbolic Systems and Kinetic Equations in the Diffusion Limit
- Numerical Methods for the Optimal Control of Scalar Conservation Laws
- Convergence of Linearized and Adjoint Approximations for Discontinuous Solutions of Conservation Laws. Part 1: Linearized Approximations and Linearized Output Functionals
- Strong Stability for Additive Runge–Kutta Methods
