A priori Error Analysis of a Discontinuous Galerkin Method for Cahn–Hilliard–Navier–Stokes Equations
Year: 2020
Author: Chen Liu, Béatrice Rivière
CSIAM Transactions on Applied Mathematics, Vol. 1 (2020), Iss. 1 : pp. 104–141
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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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/csiam-am.2020-0005
CSIAM Transactions on Applied Mathematics, Vol. 1 (2020), Iss. 1 : pp. 104–141
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 38
Keywords: Cahn–Hilliard–Navier–Stokes interior penalty discontinuous Galerkin method existence uniqueness stability error estimates.