Error estimation for the convective Cahn Hilliard equation

The Cahn-Hilliard phase-field (or diffuse-interface) model has a wide range of applications where the interest is the modelling of phase segregation and evolution of multiphase flow systems. In order to capture the physics of these systems, diffuse- interface models presume a nonzero interface thickness between immiscible constituents, see [1]. The multiscale nature inherent in these models (interface thickness and domain size of interest) urges the use of space-adaptivity in discretization. In this contribution we consider the a-posteriori error analysis of the convective Cahn- Hilliard [4] model for varying Peclet number and interface-thickness (diffusivity) parameter. The adaptive discretization strategy uses mixed finite elements, a stable time-stepping algorithm and residual-based a-posteriori error estimation [2, 5]. This analysis for the convective model forms a basic step in our research and will be helpful to the coupled Cahn-Hilliard/Navier-Stokes system [3] which is the desired model for future research.