A priori Error Analysis of a Discontinuous Galerkin Method for Cahn–Hilliard–Navier–Stokes Equations (CSIAM Transactions on Applied Mathematics, 2020)
In this paper, we analyze an interior penalty discontinuous Galerkin methodfor solving the coupled Cahn–Hilliard and Navier–Stokes equations. We prove unconditional unique solvability of the discrete system, and we derive stability bounds without any restrictions on the chemical energy density function. The numerical solutionssatisfy a discrete energy dissipation law and mass conservation laws. Convergence ofthe method is obtained by obtaining optimal a priori error estimates.
Keywords: Cahn–Hilliard–Navier–Stokes; interior penalty discontinuous Galerkin method; existence; uniqueness; stability; error estimates.