@Article{CSIAM-AM-1-1,
author = {Liu, Chen and Rivière, Béatrice},
title = {A priori Error Analysis of a Discontinuous Galerkin Method for Cahn–Hilliard–Navier–Stokes Equations},
journal = {CSIAM Transactions on Applied Mathematics},
year = {2020},
volume = {1},
number = {1},
pages = {104--141},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2708-0579},
doi = {https://doi.org/10.4208/csiam-am.2020-0005},
url = {https://global-sci.com/article/82368/a-priori-error-analysis-of-a-discontinuous-galerkin-method-for-cahnhilliardnavierstokes-equations}
}