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An $$H^1$$-Galerkin mixed finite element method combined with the modified method of characteristics for incompressible miscible displacement problems in porous media. (English) Zbl 1096.76516
Summary: An $$H^1$$-Galerkin mixed finite element procedure combined with the method of characteristics is analysed for incompressible miscible displacement problems in one-dimensional porous media. The LBB consistency condition which is a must for the approximating spaces to satisfy in the classical mixed procedures has been completely avoided. Further, a better order of convergence is derived for the concentration and computationally attractive $$C^0$$-piecewise linear polynomials can be used to approximate both the pressure and the velocity.

##### MSC:
 76M10 Finite element methods applied to problems in fluid mechanics 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 76S05 Flows in porous media; filtration; seepage