A priori Error Analysis of a Discontinuous Galerkin Method for Cahn–Hilliard–Navier–Stokes Equations

Authors

  • Chen Liu Department of Computational and Applied Mathematics, Rice University, Houston, TX 77005, USA.
  • Béatrice Rivière Department of Computational and Applied Mathematics, Rice University, Houston, TX 77005, USA.

DOI:

https://doi.org/10.4208/csiam-am.2020-0005

Keywords:

Cahn–Hilliard–Navier–Stokes, interior penalty discontinuous Galerkin method, existence, uniqueness, stability, error estimates.

Abstract

In this paper, we analyze an interior penalty discontinuous Galerkin method for 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 solutions satisfy a discrete energy dissipation law and mass conservation laws. Convergence of the method is obtained by obtaining optimal a priori error estimates.

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Published

2020-04-30

Issue

Vol. 1 No. 1 (2020)

Section

Articles