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**Numerical methods for the flow of miscible fluids in porous media.**
*(English)*
Zbl 0585.76138

Numerical methods in coupled systems, 405-439 (1984).

[For the entire collection see Zbl 0542.00019.]

The author has outlined the development of the techniques of finite element and finite difference as introduced by him and his colleagues in the last few years. The difficulties that crop up while applying these techniques are discussed along with their removal. The convergence results are also summarized. The incompressible problem is treated first and the convergence analyses for the methods are also obtained. The evaluation of methods is based on the experimental results, since all the procedures discussed converge at asymptotically optimum rates.

The author has outlined the development of the techniques of finite element and finite difference as introduced by him and his colleagues in the last few years. The difficulties that crop up while applying these techniques are discussed along with their removal. The convergence results are also summarized. The incompressible problem is treated first and the convergence analyses for the methods are also obtained. The evaluation of methods is based on the experimental results, since all the procedures discussed converge at asymptotically optimum rates.

Reviewer: Y.N.Gaur

### MSC:

76S05 | Flows in porous media; filtration; seepage |

65N06 | Finite difference methods for boundary value problems involving PDEs |

65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |

76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |