Numerical stability for finite difference approximations of Einstein's equations

Journal of Computational Physics

Volumn 218, Issue 2, 2006, Pages 607-634

  Calabrese, G ^a   Hinder, I ^a   Husa, S ^b  

^a UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

^b ALBERT EINSTEIN INSTITUT   (Germany)

Author keywords

Discrete norms; Finite difference methods; Numerical relativity; Numerical stability; Second derivatives

Indexed keywords

HAMILTONIANS; NUMERICAL METHODS; RELATIVITY; SYSTEM STABILITY;

DISCRETE NORM; EINSTEIN EQUATIONS; FINITE DIFFERENCE APPROXIMATIONS; FINITE-DIFFERENCE METHODS; FIRST ORDER; HYPERBOLIC SYSTEM; NUMERICAL RELATIVITY; SECOND DERIVATIVES; SECOND ORDERS; TIME ORDERING;

FINITE DIFFERENCE METHOD;

EID: 33748910633     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2006.02.027     Document Type: Article

References (30)

1. Shibata M., and Nakamura T. Phys. Rev. D 52 (1995) 5428
2. Baumgarte T., and Shapiro S. Phys. Rev. D 59 (1999) 024007
3. Frittelli S., and Reula O. Phys. Rev. Lett. 76 (1996) 4667
4. S.D. Hern, Ph.D. Thesis, University of Cambridge, 1999, gr-qc/0004036.
5. Anderson A., and York Jr. J.W. Phys. Rev. Lett. 82 (1999) 4384
6. Kidder L.E., Scheel M.A., and Teukolsky S.A. Phys. Rev. D 64 (2001) 064017
7. Sarbach O., Calabrese G., Pullin J., and Tiglio M. Phys. Rev. D 66 (2002) 064002
8. Nagy G., Ortiz O., and Reula O. Phys. Rev. D 70 (2004) 044012
9. Gundlach C., and Martin-Garcia J.M. Phys. Rev. D 70 (2004) 044031
10. Gundlach C., and Martin-Garcia J.M. Phys. Rev. D 70 (2004) 044032
11. Beyer H., and Sarbach O. Phys. Rev. D 70 (2004) 104004
12. Kreiss H., Petersson N., and Yström J. SIAM J. Numer. Anal. 40 (2002) 1940-1967
13. Szilágyi B., Kreiss H.-O., and Winicour J. Phys. Rev. D 71 (2005) 104035
14. Richtmyer R.D., and Morton K. Difference Methods for Initial Value Problems (1967), Interscience Publisher, New York
15. Frittelli S., and Gómez R. J. Math. Phys. 41 (2000) 5535
16. Knapp A., Walker E., and Baumgarte T. Phys. Rev. D 65 (2002) 064031
17. C. Nunn, M.phil. Thesis, University of Southampton, 2005.
18. Arnowitt R., Deser S., and Misner C. In: Witten L. (Ed). Gravitation: An Introduction to Current Research (1962), Wiley, New York
19. Bona C., Ledvinka T., Palenzuela C., and Žáček M. Phys. Rev. D 67 (2003) 104005
20. Gustafsson B., Kreiss H.-O., and Oliger J. Time Dependent Problems and Difference Methods (1995), Wiley, New York
21. Kreiss H.-O., and Lorenz J. Initial-Boundary Value Problems and the Navier-Stokes Equations (1989), Academic Press, Boston
22. Kreiss H.-O., and Scherer G. SIAM J. Numer. Anal. 29 3 (1992) 640-646
23. Kreiss H.-O., and Ortiz O.E. Lecture Notes in Physics vol. 604 (2002), Springer, New York
24. Bona C., Ledvinka T., Palenzuela C., and Žáček M. Phys. Rev. D 69 (2004) 064036
25. M. Babiuc, B. Szilágyi, J. Winicour, gr-qc/0404092.
26. Alcubierre M., et al. Class. Quantum Grav. 21 (2004) 589
27. Szilágyi B., Gómez R., Bishop N.T., and Winicour J. Phys. Rev. D 62 (2000) 104006
28. Calabrese G., Pullin J., Sarbach O., and Tiglio M. Phys. Rev. D 66 (2002) 064011
29. Calabrese G. Phys. Rev. D 71 (2005) 027501
30. Teukolsky S.A. Phys. Rev. D 61 (2000) 087501