On the approximation of miscible displacement in porous media by a method of characteristics combined with a mixed method. (English) Zbl 0661.76096

Durán, Ricardo G.

SIAM J. Numer. Anal. 25, No. 5, 989-1001 (1988).

A miscible displacement of one incompressible fluid by another is modeled by a coupled system of partial differential equations. The approximation of this system using a Galerkin method that makes use of a modified method of characteristics for the concentration equation combined with a mixed finite element method for the pressure equation has been analyzed by R. E. Ewing, Th. F. Russell and M. F. Wheeler [Comput. Math. Appl. Mech. Eng. 47, 73-92 (1984; Zbl 0535.76116; Zbl 0545.76131)].
We prove optimal error estimates in \(L^ 2\) for this algorithm under milder restrictions in the time step than those required in the previous analysis. In particular, in the two-dimensional case our estimates are valid when the time and space discretization parameter are of the same order, which is a reasonable assumption in practice.

MSC:

76S05	Flows in porous media; filtration; seepage
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65M25	Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs

Keywords:

Galerkin method; modified method of characteristics; concentration equation; optimal error estimates

Citations:

Zbl 0535.76116; Zbl 0545.76131