Computational Error Estimation and Adaptive Error Control for a Finite Element Solution of Launch Vehicle Trajectory Problems
- 1 January 1999
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Scientific Computing
- Vol. 21 (4) , 1609-1631
- https://doi.org/10.1137/s1064827599337732
Abstract
In this paper, we consider a discontinuous Galerkin finite element method for first order initial-final value problems arising from optimal control of launch vehicles. In particular, we derive an a posteriori error estimate for this method that is subsequently implemented to provide a computational error estimate used for adaptive error control. We discuss several practical issues in the implementation of the computational error estimate as well. We test the theory on a real-life trajectory problem and find that the estimates are reliable and accurate while the adaptive error control leads to a significant gain in efficiency.Keywords
This publication has 12 references indexed in Scilit:
- THE POINTWISE COMPUTABILITY OF THE LORENZ SYSTEMMathematical Models and Methods in Applied Sciences, 1998
- Control variables for finite element solution of missile trajectory optimizationJournal of Guidance, Control, and Dynamics, 1995
- Finite element method for the solution of state-constrained optimal control problemsJournal of Guidance, Control, and Dynamics, 1995
- A Posteriori Error Bounds and Global Error Control for Approximation of Ordinary Differential EquationsSIAM Journal on Numerical Analysis, 1995
- The Mathematical Theory of Finite Element MethodsPublished by Springer Nature ,1994
- Global error control for the continuous Galerkin finite element method for ordinary differential equationsESAIM: Mathematical Modelling and Numerical Analysis, 1994
- Finite element solution of optimal control problems with state-control inequality constraintsJournal of Guidance, Control, and Dynamics, 1992
- Weak Hamiltonian finite element method for optimal control problemsJournal of Guidance, Control, and Dynamics, 1991
- Toward a universal adaptive finite element strategy part 3. design of meshesComputer Methods in Applied Mechanics and Engineering, 1989
- Toward a universal adaptive finite element strategy, part 1. Constrained approximation and data structureComputer Methods in Applied Mechanics and Engineering, 1989