A monotone conservative eulerian-lagrangian scheme for reaction-diffusion- convection equations modeling chemotaxis

Numerical Methods for Partial Differential Equations

Volumn 23, Issue 3, 2007, Pages 553-586

  Smiley, Michael W ^a  

^a IOWA STATE UNIVERSITY   (United States)

Author keywords

Characteristic method; Eulerian lagrangian finite difference method; Locally mass conserving monotone method; Reaction diffusion convection equations

Indexed keywords

EID: 34248212675     PISSN: 0749159X     EISSN: 10982426     Source Type: Journal    
DOI: 10.1002/num.20185     Document Type: Article

References (18)

1. 1 E.F. Keller, L.A. Segel, Initiation of slime mold aggregation viewed as an instablity, J Theor Biol 26 ( 1970), 399–415.
2. 2 R.E. Ewing, H. Wang, A summary of numerical methods for time‐dependent advection‐dominated partial differential equations, J Comp Appl Math 128 ( 2001), 423–445.
3. 3 K.W. Morton, Numerical solution of convection‐diffusion problems, Chapman & Hall, London, 1996.
4. 4 W. Hundsdorfer, J. Verwer, Numerical solution of time‐dependent advection‐diffusion‐reaction equations, Springer‐Verlag, New York, 2003.
5. 5 J. Douglas Jr. T.F. Russell, Numerical methods for convection‐dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures, SIAM J Numer Anal 19 ( 1982), 871–885.
6. 6 R.E. Ewing, T.F. Russell, M.F. Wheeler, Simulation of miscile displacement using mixed methods and a modified method of characteristics, SPE 112241, Soc Petrol Engrg J ( 1983), 71–81.
7. 7 R.E. Ewing, T.F. Russell, M.F. Wheeler, Convergence analysis of an approximations of miscible displacelment in porous media by mixed finite elements and a modified method of characteristics, Comput Methods Appl Mech Engrg 47 ( 1984), 73–92.
8. 8 C.N. Dawson, T.F. Russell, M.F. Wheeler, Some improved error estimates for the modified method of characteristics, SIAM J Numer Anal 26 ( 1989), 1487–1512.
9. 9 M.A. Celia, T.F. Russell, I. Herrera, R.E. Ewing, An Eulerian–Lagrangian localized adjoint method for the advection‐diffusion equation, Adv Water Resour 13 ( 1990), 187–206.
10. 10 I. Herrera, R.E. Ewing, M.A. Celia, T.F. Russell, Eulerian–Lagrangian localized adjoint methods: the theoretical framework, Numer Methods Partial Differential Eq 9 ( 1993), 431–458.
11. 11 T. Arbogast, A. Chilakapati, M.F. Wheeler, A characteristic‐mixed method for contaminant transport and miscible displacement, T Russell, R. Ewing, C. Brebbia, W. Gray G. Pindar, editors, Computaional methods in water resources IX, Vol. 1: Numerical methods in water resources, Computational Mechanics Publications, Southampton, UK, 1992, pp. 77–84.
12. 12 T. Arbogast, M.F. Wheeler, A characteristics‐mixed finite element method for advection‐dominated transport problems, SIAM J Numer Anal 32 ( 1995), 404–424.
13. 13 J. Douglas Jr. F. Furtado, F. Pereira, On the numerical simulation of waterflooding of heterogeneous petroleum reservoirs, Comput Geosci 1 ( 1997), 155–190.
14. 14 J. Douglas Jr., C.‐S Huang, F. Pereira, The modified method of characteristics with adjusted advection, Technical Report, No. 298, Purdue University, 1997.
15. 15 J. Douglas Jr. F. Pereira, L. Yeh, A locally conservative Eulerian–Lagrangian numerical method and its application to nonlinear transport in porous media, Comput Geosci 4 ( 2000), 1–40.
16. 16 J. Douglas Jr. C.‐S. Huang, A locally conservative Eulerian–Lagrangian finite difference method for a parabolic equation, BIT 41 ( 2001), 480–489.
17. 17 P. Hartman, Ordinary differential equations, John Wiley & Sons, New York, 1964.
18. 18 R. Richtmyer, K. Morton, Difference Methods for Initial‐Value Problems, 2nd ed., Interscience Publishers, New York, 1967.