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math.NA2023
Numerical analysis of a hybridized discontinuous Galerkin method for the Cahn-Hilliard problem
Keegan L. A. Kirk, Rami Masi, Beatrice Riviere
The mixed form of the Cahn-Hilliard equations is discretized by the hybridizable discontinuous Galerkin method. For any chemical energy density, existence and uniqueness of the num…
math.NA2022
Discontinuous Galerkin Approximations to Elliptic and Parabolic Problems with a Dirac Line Source
Rami Masri, Boqian Shen, Beatrice Riviere
The analyses of interior penalty discontinuous Galerkin methods of any order k for solving elliptic and parabolic problems with Dirac line sources are presented. For the steady sta…
math.NA2021
Improved a priori error estimates for a discontinuous Galerkin pressure correction scheme for the Navier-Stokes equations
Rami Masri, Chen Liu, Beatrice Riviere
The pressure correction scheme is combined with interior penalty discontinuous Galerkin method to solve the time-dependent Navier-Stokes equations. Optimal error estimates are deri…