A Decoupled Energy Stable Adaptive Finite Element Method for Cahn–Hilliard–Navier–Stokes Equations (Communications in Computational Physics, 2021)
In this paper, we propose, analyze, and numerically validate an adaptivefinite element method for the Cahn–Hilliard–Navier–Stokes equations. The adaptivemethod 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 forthe fully discrete scheme. A superconvergent cluster recovery based a posteriori errorestimations are constructed for both the phase field variable and velocity field function,respectively. Based on the proposed space and time discretization error estimators, atime-space adaptive algorithm is designed for numerical approximation of the Cahn–Hilliard–Navier–Stokes equations. Numerical experiments are presented to illustratethe reliability and efficiency of the proposed error estimators and the correspondingadaptive algorithm.
Keywords: Cahn–Hilliard equation; Navier–Stokes equation; energy stability; adaptive; SCR.