Computational error estimation and adaptive error control for a finite element solution of launch vehicle trajectory problems

SIAM Journal of Scientific Computing

Volumn 21, Issue 4, 1999, Pages 1609-1631

  Estep, Donald ^a   Hodges, Dewey H ^b   Warner, Michael ^b  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b Georgia Institute of Technology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ADAPTIVE CONTROL SYSTEMS; BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; COMPUTATIONAL METHODS; DIFFERENTIAL EQUATIONS; FINITE ELEMENT METHOD; GALERKIN METHODS; OPTIMAL CONTROL SYSTEMS; PROBLEM SOLVING;

ADAPTIVE ERROR CONTROL; COMPUTATIONAL ERROR ESTIMATION; LAUNCH VEHICLE TRAJECTORY PROBLEMS;

ERROR ANALYSIS;

EID: 0033293082     PISSN: 10648275     EISSN: None     Source Type: None    
DOI: 10.1137/S1064827599337732     Document Type: Article

References (20)

1. R. BLESS, Time-Domain Finite Elements in Optimal Control with Application to Launch Vehicle Guidance, Ph.D. thesis, School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA, 1991.
2. R. BLESS AND D. HODGES, Finite element solution of optimal control problems with stat-control inequality constraints, J. Guid. Control Dyn., 15 (1992), pp. 1029-1032.
3. R. BLESS, D. HODGES, AND H. SEYWALD, Finite element method for the solution of state-constrained optimal control problems, J. Guid. Control Dyn., 18 (1995), pp. 1036-1043.
4. S. BRENNER AND L. R. SCOTT, The Mathematical Theory of Finite Element Methods, Springer-Verlag, New York, 1994.
5. A. E. BRYSON, JR. AND Y. C. Ho, Applied Optimal Control Optimization, Estimation, and Control, Hemisphere, Washington, D.C., 1975.
6. L. DEMKOWICZ, J. ODEN, W. RACHOWICZ, AND O. HARDY, Towards a universal hp adaptive finite element strategy. Part 1. Constrained approximation and data structure, Comput. Methods. Appl. Mech. Engrg., 77 (1989), pp. 79-112.
7. K. ERIKSSON, D. ESTEP, P. HANSBO, AND C. JOHNSON, Introduction to adaptive methods for differential equations, Acta Numerica, 1995, Cambridge University Press, Cambridge, UK, 1995, pp. 105-158.
8. K. ERIKSSON, D. ESTEP, P. HANSBO, AND C. JOHNSON, Computational Differential Equations, Cambridge University Press, Cambridge, UK, 1996.
9. D. ESTEP, A posteriori error bounds and global error control for approximations of ordinary differential equations, SIAM J. Numer. Anal., 32 (1995), pp. 1-48.
10. D. ESTEP AND D. FRENCH, Global error control for the continuous Galerkin finite element method for ordinary differential equations, RAIRO Modél. Math. Anal. Numér., 28 (1994), pp. 815-852.
11. D. ESTEP AND C. JOHNSON, The pointwise computability of the Lorenz system, Math. Models Methods Appl. Sci., 8 (1998), pp. 1277-1305.
12. D. ESTEP, M. LARSON, AND R. WILLIAMS, Estimating the error of numerical solutions of systems of nonlinear reaction-diffusion equations, AMS Memoirs, 1997, to appear.
13. D. HODGES AND R. BLESS, Weak Hamiltonian finite element method for optimal control problems, J. Guid. Control Dyn., 14 (1991), pp. 148-156.
14. D. HODGES AND J. M. JOHNSON, Control variables for finite element solution of missile trajectory optimization, J. Guid. Control Dyn., 18 (1995), pp. 1208-1211.
15. W. RACHOWICZ, J. ODEN, AND L. DEMKOWICZ, Towards a universal h-p adaptive finite element strategy. III. Design of h-p meshes, Comput. Methods Appl. Mech. Engrg., 77 (1989), pp. 79-112.
16. M. WARNER, Numerical Solutions to Variational Optimal Control Problems by Parallel Shooting and Costate Approximations, Master's thesis, The George Washington University, Washington, D.C., 1991.
17. M. WARNER, Numerical Solutions to Optimal-Control Problems by Finite Elements in Time with Adaptive Error Control, Ph.D. thesis, School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA, 1997.
18. M. WARNER AND D. H. HODGES, Solving boundary-value problems using hp-version finite elements in time, Internat. J. Numer. Methods Engrg., 43 (1998), pp. 425-440.
19. M. WARNER AND D. H. HODGES, Solving optimal control problems using hp-version finite elements in time, J. Guid. Control Dyn., (1999), to appear.
20. M. WARNER AND D. H. HODGES, Treatment of control constraints in finite element solution of optimal control problems, J. Guidance Control Dynamics, 22 (1999), pp. 358-360.