Abstract
In this paper, we carry out the error analysis for a totally decoupled, linear and unconditionally energy stable finite element method to solve the Cahn–Hilliard–Navier–Stokes equations. The fully finite element scheme is based on a stabilization for Cahn–Hilliard equation and projection method for Navier–Stokes equation, as well as the first order Euler method for time discretization. A priori error analysis for phase field, velocity field and pressure variable are derived for the fully discrete scheme.
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