TY - JOUR
T1 - A Decoupled Energy Stable Adaptive Finite Element Method for Cahn–Hilliard–Navier–Stokes Equations
AU - Chen , Yaoyao
AU - Huang , Yunqing
AU - Yi , Nianyu
JO - Communications in Computational Physics
VL - 4
SP - 1186
EP - 1212
PY - 2021
DA - 2021/02
SN - 29
DO - http://doi.org/10.4208/cicp.OA-2020-0032
UR - https://global-sci.org/intro/article_detail/cicp/18647.html
KW - Cahn–Hilliard equation, Navier–Stokes equation, energy stability, adaptive, SCR.
AB - <p style="text-align: justify;">In this paper, we propose, analyze, and numerically validate an adaptive
finite element method for the Cahn–Hilliard–Navier–Stokes equations. The adaptive
method is based on a linear, decoupled scheme introduced by Shen and Yang [30].
An unconditionally energy stable discrete law for the modified energy is shown for
the fully discrete scheme. A superconvergent cluster recovery based a posteriori error
estimations are constructed for both the phase field variable and velocity field function,
respectively. Based on the proposed space and time discretization error estimators, a
time-space adaptive algorithm is designed for numerical approximation of the Cahn–Hilliard–Navier–Stokes equations. Numerical experiments are presented to illustrate
the reliability and efficiency of the proposed error estimators and the corresponding
adaptive algorithm.</p>