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.
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.
