Geodesic
Convergence of a high order method in time and space for the miscible displacement equations
Li, Jizhou1 ; Riviere, Beatrice1 ; Walkington, Noel2 
1 Department of Computational and Applied Mathematics, Rice University, Houston, TX 77005, USA
2 Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213, USA
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 4, pp. 953-976

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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.

Reçu le :
DOI : 10.1051/m2an/2014059
Classification : 65M12, 65M60
Keywords: Generalized Aubin−Lions, discontinuous Galerkin, mixed finite element, arbitrary order, weak solution, convergence

Li, Jizhou 1 ; Riviere, Beatrice 1 ; Walkington, Noel 2

1 Department of Computational and Applied Mathematics, Rice University, Houston, TX 77005, USA
2 Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213, USA 
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     title = {Convergence of a high order method in time and space for the miscible displacement equations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
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Li, Jizhou; Riviere, Beatrice; Walkington, Noel. Convergence of a high order method in time and space for the miscible displacement equations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 4, pp. 953-976. doi: 10.1051/m2an/2014059

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