The modified method of characteristics with mixed finite element domain decomposition procedures for the enhanced oil recovery simulation.

*(English)*Zbl 1329.65204Summary: For the enhanced oil recovery simulation, the modified method of characteristics with mixed finite element domain decomposition procedures applicable to parallel arithmetic is put forward. The flow equation is described by the mixed finite element method and the concentration and components concentration equations are treated by the modified method of characteristics finite element domain decomposition methods. Some techniques, such as calculus of variations, domain decomposition, characteristic method, energy method, negative norm estimate and prior estimates and techniques are employed. Optimal order estimates in \(L^2\) norm are derived for the error in the approximation solution. Thus, the well-known theoretical problem has been thoroughly and completely solved.

##### MSC:

65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |

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

65Y05 | Parallel numerical computation |

78A25 | Electromagnetic theory (general) |