Convergence of high order methods for miscible displacement
Yekaterina Epshteyn 1, Beatrice Riviére 21 Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA
2 Department of Mathematics, University of Pittsburgh, 301 Thackeray, Pittsburgh, PA 15260, USA
Received by the editors September 24, 2007
We derive error estimates for fully discrete scheme using primal discontinuous Galerkin discretization in space and backward Euler discretization in time. The estimates in the energy norm are optimal with respect to the mesh size and suboptimal with respect to the polynomial degree. The proposed scheme is of high order as polynomial approximations of pressure and concentration can take any degree. In addition, the method can handle different types of boundary conditions ana is well-suited for unstructured meshes.
AMS subject classifications: 35Q35, 65N30, 65N15, 76S05
Key words: flow; transport; porous media; miscible displacement; NIPG; SIPG; IIPG; h and p-version; fully discrete scheme
Email: firstname.lastname@example.org (Y. Epshteyn), email@example.com (B. Riviére)