Seminar Details
2006-07-11 (15.00 pm) : "A discontinuous Galerkin finite element method for the Cahn Hilliard Equation"
At Euler building
Organized by Mathematical Engineering
Speaker :
Krishna Garikipati (University of Michigan)
Abstract :
Written originally to model phase separation in binary alloys, the Cahn-Hilliard
Equation has also been applied to problems as diverse as multi-phase fluid flow, image processing,
planet formation and pattern formation in biology. It is a parabolic partial differential with an instability-promoting
second-order spatial derivative, but is stabilized by a fourth-order derivative. The competition between these terms
leads to the formation of diffuse interfaces with tunable thickness. This equation has also spawned a burgeoning
mathematical literature. In this talk I will introduce this equation from a physical standpoint, and proceed to a
discontinuous Galerkin (DG) finite element method designed to treat the high-order derivatives. The crux of the
talk is that $C0$ interpolation functions are sufficient in the DG setting despite the high-order derivatives. The weak form
of the problem is the point of departure for proving convergence of the method, and stability of the time-discrete solutions.
Several numerical examples will also be presented.