**Some Computational Issues in
Oil Reservoir Studies**

In tertiary oil recovery, an inexpensive fluid is injected into the reservoir
so as to mix with the hydrocarbon (oil) and then to push the resulting fluid
towards the production wells. Assuming there is no volume change and the fluid
is slightly compressible, the mathematical model gives rise to a coupled system
of parabolic equations: one in pressure and the other one in concentration.
Since the concentration equation is convection dominated and depends mainly on
velocity not pressure, the following issues are addressed in [26],[30] (in the
list of publications) and [1], [6], [8] (Submitted Manuscripts and Thesis
of Mr. M. A. Mohamed Ali):

1. H1-mixed finite element method.

2. C0-interior penalty method and modified method of characteristics (exclusively for convection dominated
diffusion problems).

3. Incomplete time stepping with preconditioning (to solve efficiently the resulting large system of
equations).

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