1 Department of Computational and
Applied Mathematics, Rice University, Houston, TX
2 Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213, USA
Revised: 30 October 2014
A numerical method is formulated and analyzed for solving the miscible displacement problem under low regularity assumptions. The scheme employs discontinuous Galerkin time stepping with mixed and interior penalty discontinuous Galerkin finite elements in space. The numerical approximations of the pressure, velocity, and concentration converge to the weak solution as the mesh size and time step tend to zero. To pass to the limit a compactness theorem is developed which generalizes the Aubin−Lions theorem to accommodate discontinuous functions both in space and in time.
Mathematics Subject Classification: 65M12 / 65M60
Key words: Generalized Aubin−Lions / discontinuous Galerkin / mixed finite element / arbitrary order / weak solution / convergence
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