Numerical analysis of a discontinuous Galerkin method for Cahn-Hilliard-Navier-Stokes equations
This work offers rigorous numerical analysis for a complex multiphase flow model, benefiting computational mathematicians and engineers.
The authors provide a theoretical analysis of a discontinuous Galerkin method for the Cahn-Hilliard-Navier-Stokes equations, proving unconditional solvability, energy dissipation, and optimal error estimates.
In this paper, we derive a theoretical analysis of an interior penalty discontinuous Galerkin methods for solving the Cahn-Hilliard-Navier-Stokes model problem. We prove unconditional unique solvability of the discrete system, obtain unconditional discrete energy dissipation law, and derive stability bounds with a generalized chemical energy density. Convergence of the method is obtained by proving optimal a priori error estimates. Our analysis of the unique solvability is valid for both symmetric and non-symmetric versions of the discontinuous Galerkin formulation.