Numerical analysis of a discontinuous Galerkin method for Cahn-Hilliard-Navier-Stokes equations

2018/07/07 by Chen Liu, Liu, Chen, Béatrice Rivière +1
Engineering · Materials Science · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Numerical Analysis (math.NA) #Solidification and crystal growth phenomena

paper · pdf · doi:10.48550/arxiv.1807.02725

openalex publication_date 2018/07/07 · openalex created_date 2018/07/19 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Finite Element Approximation of the Cahn--Hilliard Equation with Degenerate Mobility
• On Linear and unconditionally energy stable Algorithms for Variable Mobility Cahn-Hilliard Type Equation with Logarithmic Flory-Huggins Potential

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