Browsing by Author "Walkington, Noel"

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    Convergence of a Discontinuous Galerkin Method For the Miscible Displacement Under Minimal Regularity
    (2009-05) Rivière, Béatrice M.; Walkington, Noel
    Discontinuous Galerkin time discretizations are combined with the mixed finite element and continuous finite element methods to solve the miscible displacement problem. Stable schemes of arbitrary order in space and time are obtained. Under minimal regularity assumptions on the data, convergence of the scheme is proved by using compactness results for functions that may be discontinuous in time.
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    Convergence of a high order method in time and space for the miscible displacement equations
    (EDP Sciences, 2015) Li, Jizhou; Riviere, Beatrice; Walkington, Noel
    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.