Natasha S. Sharma

The University of Texas at El Paso, USA.

We consider a continuous interior penalty finite element approximation of a sixth order Cahn-Hilliard type equation which models the dynamics of phase transitions in ternary oil-water-surfactant systems. The temporal discretization is chosen so that a discrete energy law can be established leading to unconditional energy stability. Additionally, we show that the numerical method is unconditionally uniquely solvable. We conclude the talk with several numerical experiments demonstrating the unconditional stability and first order accuracy of the proposed scheme..