Pictured above is a typical example of spinodal decomposition modeled via the Cahn-Hilliard equation. The pictures were produced in MATLAB with the use of the FELICITY MATLAB/C++ Toolbox. Much of my research centers around Finite Element Methods relating to the Cahn-Hilliard equation. This equation has become an important tool in what are known as diffuse interface models. If you would like to know more, please see my research statement Research Statement. There are many branches of my research and I provide a list of current projects and past publications below.
An Efficient Solver for a Mixed Finite Element Method for the Cahn-Hilliard Equation -- Collaborators: Dr. Susanne Brenner, Dr. Li-yeng Sung
A Cahn-Hilliard Ericksen Model for Liquid Crystal Droplets -- Collaborators: Dr. Shawn Walker
Convergence Analysis and Error Estimates for a Second Order Accurate Finite Element Method for the Cahn-Hilliard-Navier-Stokes System, A. Diegel, C. Wang, X. Wang, S. Wise, Numer. Math, (Online) DOI:10.1007/s00211-017-0887-5 Download PDF
Stability and Convergence of a Second Order Mixed Finite Element Method for the Cahn-Hilliard Equation, A. Diegel, C. Wang, S. Wise, IMA J. Numer. Anal. 36 (2016) 1867–1897. Download PDF
Analysis of a Mixed Finite Element Method for a Cahn–Hilliard–Darcy–Stokes System, A. Diegel, X. Feng, S. Wise, SIAM J. Numer. Anal. 53 (2015) 127–152. Download PDF