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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
Convergence of a Decoupled Splitting Scheme for the Cahn-Hilliard-Navier-Stokes System
Chen Liu, Rami Masri, Beatrice Riviere
This paper is devoted to the analysis of an energy-stable discontinuous Galerkin algorithm for solving the Cahn-Hilliard-Navier-Stokes equations within a decoupled splitting framew…
math.NA2021
A discontinuous Galerkin pressure correction scheme for the incompressible Navier-Stokes equations: stability and convergence
Rami Masri, Chen Liu, Beatrice Riviere
A discontinuous Galerkin pressure correction numerical method for solving the incompressible Navier-Stokes equations is formulated and analyzed. We prove unconditional stability of…