Sixth-Order Phase Field models serve as an effective tool in capturing the dynamics of grain growth of a polycrystal in a supercooled liquid as well as capturing the static properties of ternary oil-water-surfactant systems. Examples of promising applications include oil recovery, drug delivery systems and crack propagation in a ductile material. Despite its applications, a major challenge impeding their use has been and continues to be, a lack of understanding of these complex systems. In this talk, we present a continuous interior penalty Galerkin (C0-IP) framework for solving these equations and theoretically establish the desirable properties of stability, unique solvability and convergence. We close the talk by presenting the numerical results of some benchmark problems to verify the practical performance of the proposed approach and discuss some exciting current and future applications.

This is a joint work with Amanda Diegel from Mississippi State University. It is funded by National Science Foundation DMS 2110774 and the HPC resources are provided by Texas Advanced Computing Center (TACC).

Place: Math, 402 and
Zoom   https://arizona.zoom.us/j/83758253931
Password:  applied