Adaptive moving mesh computations for reaction-diffusion systems

Journal of Computational and Applied Mathematics

Volumn 168, Issue 1-2, 2004, Pages 519-528

  Zegeling, P A ^a   Kok, H P ^a  

^a UTRECHT UNIVERSITY   (Netherlands)

Author keywords

Adaptive mesh refinement; Finite differences; Method of lines; Moving mesh; Pattern formation; Reaction diffusion equations

Indexed keywords

ADAPTIVE SYSTEMS; COORDINATION REACTIONS; DIFFUSION; MATHEMATICAL MODELS; NUMERICAL ANALYSIS;

ADAPTIVE MOVING MESH; COORDINATE TRANSFORMATIONS; MESH COMPUTATIONS;

PARTIAL DIFFERENTIAL EQUATIONS;

MATHEMATICAL ANALYSIS;

EID: 2942517483     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2003.06.013     Document Type: Article

References (18)

1. Beckett G. Mackenzie J.A. Ramage A. Sloan D.M. Computational solution of two-dimensional unsteady PDEs using moving mesh methods J. Comput. Phys. 182 2002 478-495
2. Carlson N. Miller K. Design and application of a gradient-weighted moving finite element code II: in two dimensions SIAM J. Sci. Comput. 19 1998 766-798
3. Clement Ph. Hagmeijer R. Sweers G. On the invertibility of mappings arising in 2D grid generation problems Numer. Math. 73 1996 37-51
4. Doelman A. Kaper T.J. Zegeling P.A. Pattern formation in the one-dimensional Gray-Scott model Nonlinearity 10 1997 523-563
5. Hairer E. Nørsett S.P. Wanner G. Solving Ordinary Differential Equations, I. Nonstiff Problems 1987 Springer Berlin
6. Huang W. Russell R.D. A high dimensional moving mesh strategy Appl. Numer. Math. 26 1997 63-76
7. Huang W. Russell R.D. Moving mesh strategy based on a gradient flow equation for two-dimensional problems SIAM J. Sci. Comput. 3 1999 998-1015
8. Knupp P. Steinberg S. The Fundamentals of Grid Generation 1993 CRC Boca Raton, FL
9. Liseikin V.D. Grid Generation Methods 1999 Springer Berlin
10. Liu F. Ji S. Liao G. An adaptive grid method and its application to steady Euler flow calculations SIAM J. Sci. Comput. 20 1998 811-825
11. Nicolis G. Prigogine I. Exploring Complexity 1989 Freeman New York
12. Pearson J.A. Complex patterns in a simple system Science 261 1993 189-192
13. Ruuth S.J. Implicit-explicit methods for reaction-diffusion problems in pattern formation J. Math. Biol. 34 1995 148-176
14. Tang H.Z. Tang T. Adaptive mesh methods for one- and two-dimensional hyperbolic conservation laws SIAM J. Numer. Anal. 41 2003 487-515
15. A. Vande Wouwer, Ph. Saucez, W.E. Schiesser (Eds.), Adaptive Method of Lines, CRC, Boca Raton, FL, 2001.
16. van der Vorst H.A. Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems SIAM J. Sci. Statist. Comput. 3 1992 631-644
17. A.M. Winslow, Adaptive mesh zoning by the equipotential method, Technical Report UCID 19062, 1981.
18. Zegeling P.A. Keppens R. Adaptive MOL for magneto-hydrodynamic PDE models Wouwer A.V. Saucez P. Schiesser W.E. Adaptive Method of Lines 2001 117-137 Chapman - Hall/CRC London/Boca Raton, FL