Dynamical systems flow computation by adaptive triangulation methods

Computing and Visualization in Science

Volumn 2, Issue 1, 1999, Pages 15-24

  Stämpfle, Martin ^a  

^a UNIVERSITY OF ULM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMICAL SYSTEMS; TRIANGULATION;

DOMAIN METHODS; FLOW COMPUTATION; IMAGE METHOD; LORENZ EQUATION; NEW APPROACHES; NUMERICAL COMPUTATIONS; TRIANGULATION METHOD;

NUMERICAL METHODS;

EID: 0003073423     PISSN: 14329360     EISSN: 14330369     Source Type: Journal    
DOI: 10.1007/s007910050023     Document Type: Article

References (21)

1. Castillo, J.E. (ed.): Mathematical Aspects of Numerical Grid Generation. Philadelphia: SIAM 1991
2. Chui, C.K., Lai, M.-J.: Multivariate vertex splines and finite elements. J. Approx. Theory 60, 245-343 (1990)
3. D'Azevedo, E.F.: Optimal triangular mesh generation by coordinate transformation. SIAM J. Sci. Stat. Comput. 12, 755-786 (1991)
4. D'Azevedo, E.F., Simpson, R.B.: On optimal triangular meshes for minimizing the gradient error. Numer. Math. 59, 321-348 (1991)
5. De Boor, C.: A Practical Guide to Splines. New York: Springer 1978
6. Hindmarsh, A.C., Petzold, L.R.: ODEPACK - a program package for solving ordinary differential equations (Version 87, Livermore 1987). Livermore 1983
7. Lorenz, E.N.: Deterministic nonperiodic flow. J. Atmospheric Science 20, 130-141 (1963)
8. Macki, J., Strauss, A.: Introduction to Optimal Control Theory. New York: Springer 1982
9. Nielson, G.M., Hagen, H., Müller, M.: Scientific Visualization - Overviews, Methodologies, Techniques. IEEE Comp. Soc., Los Alamitos, 1997
10. Rheinboldt, W.C.: On a theory of mesh-refinement processes. SIAM J. Numer. Anal. 17, 766-778 (1980)
11. Rheinboldt, W.C.: Adaptive mesh refinement processes for finite element solutions. Int. J. Numer. Meth. Eng. 17, 649-662 (1981)
12. Rivara, M.-C: Selective refinement=derefinement algorithms for sequences of nested triangulations. Int. J. Numer. Meth. Eng. 28, 2889-2906 (1989)
13. Rivara, M.-C: Local modification of meshes for adaptive and/or multigrid finite-element methods. J. Comput. Appl. Math. 36, 79-89 (1991)
14. Rüde, U.: Mathematical and Computational Techniques for Multilevel Adaptive Methods. Philadelphia: SIAM 1993
15. Seydel, R.: BIFPACK - a program package for calculating bifurcations (Version 3.1, Ulm 1996). Buffalo 1983
16. Seydel, R.: Practical Bifurcation and Stability Analysis: From Equilibrium to Chaos (Second Edition). New York: Springer 1994
17. Stämpfle, M.: Controlling chaos through iteration sequences and interpolation techniques. Int. J. Bifurcation and Chaos 4(6), 1697-1701 (1994)
18. Stämpfle, M.: Numerische Approximation des Flusses eines dynamischen Systems mit adaptiven Triangulierungsverfahren. Aachen: Shaker 1998
19. Stämpfle, M.: Optimal estimates for the linear interpolation error on simplices. Submitted to J. Approx. Theory, 1998
20. Stämpfle, M.: Computing the flow of dynamical systems with adaptive triangulation methods. Contributed Talk, ICIAM 99, Edinburgh, 1999
21. Ziegler, G.M.: Lectures on Polytopes. New York: Springer 1995