Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

An efficient numerical scheme for precise time integration of a diffusion-dissolution/precipitation chemical system


Authors: Blaise Faugeras, Jérôme Pousin and Franck Fontvieille
Journal: Math. Comp. 75 (2006), 209-222
MSC (2000): Primary 65M12, 65G99, 35K57
DOI: https://doi.org/10.1090/S0025-5718-05-01782-5
Published electronically: September 29, 2005
MathSciNet review: 2176396
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A numerical scheme based on an operator splitting method and a dense output event location algorithm is proposed to integrate a diffusion-dissolution/precipitation chemical initial-boundary value problem with jumping nonlinearities. The numerical analysis of the scheme is carried out and it is proved to be of order 2 in time. This global order estimate is illustrated numerically on a test case.


References [Enhancements On Off] (What's this?)

  • 1. C. Besse, B. Bidegaray, and S. Descombes, Order estimates in time of splitting methods for the nonlinear schrödinger equation, SIAM J. Numer. Anal. 40 (2002), no. 5, 26-40. MR 1921908 (2003k:65099)
  • 2. S. Descombes, Convergence of a splitting method of high order for reaction-diffusion systems, Math. Comp. 70 (2001), no. 236, 1484-1501.MR 1836914 (2002c:65152)
  • 3. S. Descombes and M. Massot, Operator splitting for nonlinear reaction-diffusion systems with an entropic structure : singular perturbation and order reduction, Numerische Mathematik (2004) Vol. 97, No. 4, 667-698.
  • 4. E. Hairer, S.P. Norsett, and G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems, Springer Series in Computational Mathematics, Springer Verlag, 1993. MR 1227985 (94c:65005)
  • 5. E. Hairer and G. Wanner, Solving Ordinary Differential Equations II, Stiff and Differential-Algebraic Problems, Springer Series in Computational Mathematics, Springer Verlag, 1993. MR 1111480 (92a:65016)
  • 6. C. Lubich and T. Jahnke, Error bounds for exponential operator splitting, Technical report, Universitat Tubingen, Germany, 1999; BIT 40 (2000), 735-744.MR 1799313 (2001k:65143)
  • 7. E. Maisse, Analyse et simulations numériques de phénomènes de diffusion-dissolution/précipitation en milieux poreux, appliquées au stockage de déchets, Ph.D. thesis, Université Claude Bernard Lyon I, 1998.
  • 8. E. Maisse and J. Pousin, Diffusion and dissolution/precipitation in an open porous reactive medium, J. Comp. Appl. Math. 82 (1997), 279-280.MR 1473546 (98g:35170)
  • 9. G.I. Marchuk, Splitting and alternating direction methods, Handbook of numerical analysis, vol. I, North-Holland, Amsterdam, 1990, pp. 197-462. MR 1039325
  • 10. M. Schatzman, Toward non commutative numerical analysis : high order integration in time, Journal of Scientific Computing 17 (2002), no. 1-3, 107-125. MR 1910554
  • 11. L.F. Shampine, Interpolation for Runge-Kutta methods, SIAM J. Numer. Anal. 22 (1985), 1014-1027. MR 0799125 (86j:65014)
  • 12. B. Sportisse, An analysis of operator splitting techniques in the stiff case, J. Comput. Phys. 161 (2000), no. 1, 140-168. MR 1762076 (2001f:65107)
  • 13. G. Strang, On the construction and comparison of difference schemes, SIAM J. Numer. Anal. 5 (1968), 506-517. MR 0235754 (38:4057)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 65M12, 65G99, 35K57

Retrieve articles in all journals with MSC (2000): 65M12, 65G99, 35K57


Additional Information

Blaise Faugeras
Affiliation: CNRS I35, Les Algorithmes, 2000 Route des Lucioles, BP 121, 06903 Sophia Antipolis cedex France
Email: Blaise.Faugeras@unice.fr

Jérôme Pousin
Affiliation: MAPLY, Centre de Mathématique INSA de Lyon, Bat. Léonard de Vinci, 21, Av. Jean Capelle, 69100 Villeurbanne Cedex, France
Email: Jerome.Pousin@insa-lyon.fr

Franck Fontvieille
Affiliation: MAPLY, Centre de Mathématique INSA de Lyon, Bat. Léonard de Vinci, 21, Av. Jean Capelle, 69100 Villeurbanne Cedex, France
Email: Franck.Fontvieille@insa-lyon.fr

DOI: https://doi.org/10.1090/S0025-5718-05-01782-5
Keywords: Numerical time integration, operator splitting, dense output, high order, error analysis, reaction-diffusion, jumping nonlinearities
Received by editor(s): December 2, 2003
Received by editor(s) in revised form: September 20, 2004
Published electronically: September 29, 2005
Article copyright: © Copyright 2005 American Mathematical Society

American Mathematical Society