Superconvergence for a time-discretization procedure for the mixed finite element approximation of miscible displacement in porous media



A time-stepping procedure is established and analyzed for the problem of miscible displacement in porous medium. The fluid velocity based on mixed element method is post-processed by interpolation along Gauss lines. Error analysis shows that this procedure has a superconvergence error bound O(hmath image) with respect to the parameter hp, which is one order higher than the conventional Galerkin or mixed finite element procedures. Compared with the results in the references, the parameter constraint conditions in this article are obviously relaxed. © 2011Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2012