Li, JizhouRiviere, BeatriceWalkington, Noel2016-02-022016-02-022015Li, Jizhou, Riviere, Beatrice and Walkington, Noel. "Convergence of a high order method in time and space for the miscible displacement equations." <i>ESAIM: M2AN,</i> 49, no. 4 (2015) EDP Sciences: 953-976. http://dx.doi.org/10.1051/m2an/2014059.https://hdl.handle.net/1911/88306A 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.engArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.Journal articleGeneralized Aubin-Lionsdiscontinuous Galerkinmixed finite elementarbitrary orderweak solutionconvergencehttp://dx.doi.org/10.1051/m2an/2014059