TY - JOUR
T1 - A priori Error Analysis of a Discontinuous Galerkin Method for Cahn–Hilliard–Navier–Stokes Equations
AU - Liu , Chen
AU - Rivière , Béatrice
JO - CSIAM Transactions on Applied Mathematics
VL - 1
SP - 104
EP - 141
PY - 2020
DA - 2020/03
SN - 1
DO - http://doi.org/10.4208/csiam-am.2020-0005
UR - https://global-sci.org/intro/article_detail/csiam-am/16795.html
KW - Cahn–Hilliard–Navier–Stokes, interior penalty discontinuous Galerkin method, existence, uniqueness, stability, error estimates.
AB - <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>