Finite volume element approximations of nonlocal reactive flows in porous media

Numerical Methods for Partial Differential Equations

Volumn 16, Issue 3, 2000, Pages 285-311

  Ewing, Richard ^a   Lazarov, Raytcho ^a   Lin, Yanping ^b  

^a TEXAS A AND M UNIVERSITY   (United States)

^b UNIVERSITY OF ALBERTA   (Canada)

Author keywords

Control volume; Finite volume element; NonFickian flows; error estimates

Indexed keywords

EID: 0001205239     PISSN: 0749159X     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1098-2426(200005)16:3<285::AID-NUM2>3.0.CO;2-3     Document Type: Article

References (31)

1. J. H. Cushman, Nonlocal dispersion in media with continuously evolving scales of heterogeneity, Transport Porous Media 13 (1993), 123-138.
2. J. H. Cushman, X. Hu, and F. Deng, Nonlocal reactive transport with physical and chemical heterogeneity: Localization error, Water Resource Res 31 (1995), 2219 2237.
3. J. H. Cushman and T. R. Ginn, Nonlocal dispersion in media with continuously evolving scales of heterogeneity. Transport Porous Media 13 (1993), 123-138.
4. G. Dagan, The significance of heterogeneity of evolving scales to transport in porous formations, Water Resource Res 30 (1994), 3327-3336.
5. V. V. Shelukhin, A non-local in time model for radionuclides propagation in Stokes fluids, Dynamics of fluids with free boundaries, Siberian Russian Acad Sci, Inst Hydrodynam 107 (1993), 180-193.
6. M. Renardy, W. Hrusa, and J. A. Nohel, Mathematical problems in viscoelasticity, Longman Sci Tech, England, 1987.
7. W. Allegretto, Y. Lin, and A. Zhou, A box scheme for coupled systems resulting from micro-sensor thermistor problems, Dynam Discr Contin Impuls Sys 5 (1999), 209-223.
8. 1-projection and Galerkin methods for nonlinear parabolic integro-differential equations, Calcolo 25 (1988), 187-201.
9. Y. Lin, V. Thomée, and L. Wahlbin, Ritz-Volterra projection onto finite element spaces and application to integro-differential and related equations, SIAM J Numer Anal 28 (1995), 1047-1070.
10. Y. Lin, On maximum norm estimates for Ritz-Volterra projections and applications to some time-dependent problems, J Comp Math 15 (1997), 159-178.
11. I. H. Sloan and V. Thomée, Time discretization of an integro-differential equation of parabolic type, SIAM J Numer Anal 23 (1986), 1052-1061.
12. T. Zhang, The stability and approximation properties of Ritz-Volterra projection and application, I, Numer Math J Chinese Univ Eng Ser 6 (1997), 57-76.
13. R. E. Bank and D. J. Rose, Some error estimates for the box method, SIAM J Numer Anal 24 (1987), 777-787.
14. Z. Cai, On the finite volume element method, Numer Math 58 (1991), 713-735.
15. Z. Cai and S. McCormick, On the accuracy of the finite volume element method for diffusion equations on composite grids, SIAM J Numer Anal 27 (1990), 636-655.
16. W. Hackbusch, On first and second order box schemes, Computing 41 (1989), 277-296.
17. H. Jianguo and X. Shitong, On the finite volume element method for general self-adjoint elliptic problems, SIAM J Numer Anal 35 (1998), 1762-1774.
18. R. H. Li and Z. Y. Chen, The generalized difference method for differential equations, Jilin Univ Publ, 1994.
19. I. D. Mishev, Finite volume methods on Voronoi meshes, Numer Meth PDEs 14 (1998), 193-212.
20. R. Rannacher and L. R. Scott, Some optimal error estimates for piecewise linear finite element approximations, Math Comp 38 (1982), 1-22.
21. Q. Zu and Q. Lin, Superconvergence theory for finite element methods, Hunan Sei, Changsha, 1989
22. I. D. Mishev, Finite volume and finite volume element methods for non-symmetric problems, Texas A&M Univ, Ph.D. thesis, 1997, Tech Rept ISC-96-04-MATH.
23. B. R. Baliga and S. V. Patankar, A new finite-element formulation for convection-diffusion problems, Numer Heat Transfer 3 (1980), 393-409.
24. A. A. Samarskii, R. D. Lazarov, and V. L. Makarov, Finite difference schemes for differential equations with generalized solutions, Visshaya Shkola, Moscow, 1987 (in Russian).
25. Q. Lin and J. Xu, Linear finite elements with high accuracy, J Comp Math 3 (1985), 115-133.
26. 2-error estimates for finite element methods for nonlinear diffusion equations with memory, SIAM J Numer Anal 27 (1990), 595-607.
27. R. E. Ewing, R. D. Lazarov, and Y. Lin, Finite volume element approximations of non-local in time one-dimensional reactive flows in porous media, Tech Rept ISC-98-06-MATH, Computing, to appear.
28. A. N. Tikhonov and A. A. Samarskii, Homogeneous difference schemes, Zh Vychisl Mat i Mat Fiz 1 (1961), 5-63.
29. A. N. Tikhonov and A. A. Samarskii, Homogeneous difference schemes on nonuniform nets, Zh Vychisl Mat i Mat Fiz 2 (1962), 812-832.
30. V. Thomée, Galerkin finite element methods for parabolic problems, Lect Notes Math, Springer-Verlag 1054 (1984).
31. V. Thomée and L. Wahlbin, Long-time numerical solution of a parabolic equation with memory, Math Comp 62 (1994), 477-496.