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 JAMP  Vol.3 No.1 , January 2015
Characteristics Collocation Method of Compressible Miscible Displacement with Dispersion
Abstract: The compressible miscible displacement in a porous media is considered in this paper. The problem is a nonlinear system with dispersion in non-periodic space. The concentration is treated by a characteristics collocation method, and the pressure is treated by an orthogonal collocation method. Optimal order estimates are derived.
Cite this paper: Ma, N. and Lu, X. (2015) Characteristics Collocation Method of Compressible Miscible Displacement with Dispersion. Journal of Applied Mathematics and Physics, 3, 86-91. doi: 10.4236/jamp.2015.31012.
References

[1]   Douglas Jr., J. and Roberts, J.E. (1983) Numerical Methods for a Model for Compressible Miscible Displacement in Porous Media. Math. Comp., 41, 441-459. http://dx.doi.org/10.1090/S0025-5718-1983-0717695-3

[2]   Russell, T.F. (1985) Time Stepping along Characteristics with Incomplete Iteration for a Galerkin Approximation of Miscible Dis-placement in Porous Media. SIAM. J Numer. Anal., 17, 970-1013. http://dx.doi.org/10.1137/0722059

[3]   Dougals, J. and Dupont, T. (1974) Lecture Notes in Math. Vol. 385, Springer-Verlag, Berlin.

[4]   Fernandes, R.L. and Fairweather, G. (1993) Analysis of Alternating Direction Collocation Methods for Parabolic and Hyperbolic Problems in Two Space Variables. Numerical Methods for Partial Differential Equations, 9, 191-211. http://dx.doi.org/10.1002/num.1690090207

[5]   Bialecki, B. and Cai, X. (1994) H1-Norm Error Bounds for Piecewise Hermite Bicubic Orthogonal Space Collocation Schemes for Elliptic Boundary Value Problems. SIAM. J Numer.Anal., 31, 1128-1146. http://dx.doi.org/10.1137/0731059

[6]   Ma, N., Lu, T. and Yang, D. (2006) Analysis of Incompressible Miscible Dis-placement in Porous Media by a Characteristics Collation Method. Numer. Methods for Partial Differential Eq., 22, 797-814.

[7]   Yuan, Y. (1992) Time Stepping along Characteristics for the Finite Element Approximation of Com-pressible Miscible Displacement in Porous Media. Mathematica Numerica Sinica, 14, 385-400.

[8]   Ma, N. (1906) Orthogonal Collocation Method for Miscible Displacement with Dispersion. Journal of Shandong University (Natural Science), 46, 78-81.

[9]   Douglas Jr., J. and Roberts, J.E. (1983) Numerical Methods for a Model for Compressible Miscible Displacement in Porous Media. Math. Comp., 41, 441-459. http://dx.doi.org/10.1090/S0025-5718-1983-0717695-3

[10]   Russell, T.F. (1985) Time Stepping along Characteristics with Incomplete Iteration for a Galerkin Approximation of Miscible Dis-placement in Porous Media. SIAM. J Numer. Anal., 17, 970-1013. http://dx.doi.org/10.1137/0722059

[11]   Dougals, J. and Dupont, T. (1974) Lecture Notes in Math. Vol. 385, Springer-Verlag, Berlin.

[12]   Fernandes, R.L. and Fairweather, G. (1993) Analysis of Alternating Direction Collocation Methods for Parabolic and Hyperbolic Problems in Two Space Variables. Numerical Methods for Partial Differential Equations, 9, 191-211. http://dx.doi.org/10.1002/num.1690090207

[13]   Bialecki, B. and Cai, X. (1994) H1-Norm Error Bounds for Piecewise Hermite Bicubic Orthogonal Space Collocation Schemes for Elliptic Boundary Value Problems. SIAM. J Numer.Anal., 31, 1128-1146. http://dx.doi.org/10.1137/0731059

[14]   Ma, N., Lu, T. and Yang, D. (2006) Analysis of Incompressible Miscible Dis-placement in Porous Media by a Characteristics Collation Method. Numer. Methods for Partial Differential Eq., 22, 797-814.

[15]   Yuan, Y. (1992) Time Stepping along Characteristics for the Finite Element Approximation of Com-pressible Miscible Displacement in Porous Media. Mathematica Numerica Sinica, 14, 385-400.

[16]   Ma, N. (1906) Orthogonal Collocation Method for Miscible Displacement with Dispersion. Journal of Shandong University (Natural Science), 46, 78-81.

 
 
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