- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 521835, 8 pages
A Finite Difference Scheme for Compressible Miscible Displacement Flow in Porous Media on Grids with Local Refinement in Time
School of Mathematic and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250014, China
Received 19 October 2012; Accepted 19 December 2012
Academic Editor: Xinan Hao
Copyright © 2013 Wei Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Y. R. Yuan, “Some new progress in the fileds of computational petroleum geology and others,” Chinese Journal of Computational Physics, vol. 20, no. 4, pp. 283–290, 2003.
- R. E. Ewing, R. D. Lazarov, and P. S. Vassilevski, “Local refinement techniques for elliptic problems on cell-centered grids. I. Error analysis,” Mathematics of Computation, vol. 56, no. 194, pp. 437–461, 1991.
- Z. Q. Cai, J. Mandel, and S. F. McCormick, “The finite volume element method for diffusion equations on general triangulations,” SIAM Journal on Numerical Analysis, vol. 28, no. 2, pp. 392–402, 1991.
- Z. Q. Cai and S. F. McCormick, “On the accuracy of the finite volume element method for diffusion equations on composite grids,” SIAM Journal on Numerical Analysis, vol. 27, no. 3, pp. 636–655, 1990.
- R. E. Ewing, R. D. Lazarov, and P. S. Vassilevski, “Finite difference schemes on grids with local refinement in time and space for parabolic problems. I. Derivation, stability, and error analysis,” Computing, vol. 45, no. 3, pp. 193–215, 1990.
- R. E. Ewing, R. D. Lazarov, and A. T. Vassilev, “Finite difference scheme for parabolic problems on composite grids with refinement in time and space,” SIAM Journal on Numerical Analysis, vol. 31, no. 6, pp. 1605–1622, 1994.
- W. Liu and Y. R. Yuan, “Finite difference schemes for two-dimensional miscible displacement flow in porous media on composite triangular grids,” Computers & Mathematics with Applications, vol. 55, no. 3, pp. 470–484, 2008.
- W. Liu and Y. R. Yuan, “A finite difference scheme for two-dimensional semiconductor device of heat conduction on composite triangular grids,” Applied Mathematics and Computation, vol. 218, no. 11, pp. 6458–6468, 2012.
- J. Douglas, Jr. and J. E. Roberts, “Numerical methods for a model for compressible miscible displacement in porous media,” Mathematics of Computation, vol. 41, no. 164, pp. 441–459, 1983.
- R. Yi Yuan, “Time stepping along charcteristics for the finite element approximation of compressible miscible displacement in porous media,” Mathematica Numerica Sinica, vol. 14, no. 4, pp. 385–406, 1992.
- J. M. Yang and Y. P. Chen, “A priori error analysis of a discontinuous Galerkin approximation for a kind of compressible miscible displacement problems,” Science China, Mathematics, vol. 53, no. 10, pp. 2679–2696, 2010.