Monday, 28 October, 2013
SPEAKER: Ms Amanda Diegel, UTK
TITLE: A Mixed Finite Element Method for a Cahn-Hilliard-Darcy-Stokes System
ABSTRACT: I consider a mixed finite element method for a modified Cahn-Hilliard equation coupled with a non-steady Darcy-Stokes flow that models phase separation and coupled fluid flow in immiscible binary fluids and diblock copolymer melts. The time discretization is based on a convex splitting of the energy of the equation. We prove that our scheme is unconditionally energy stable with respect to a spatially discrete analogue of the continuous free energy of the system, unconditionally uniquely solvable, and convergent with optimal rates in both two and three space dimensions.