Mathematical Sciences: Finite Element Method for Nonlinear Partial Differential Equations

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This research project will study the nonlinear fourth order evolutionary Cahn-Hilliard equation. A main concern will be the development of an appropriate numerical method for accurate approximation of solutions of this equation for both one and two spatial dimensions. A efficient numerical scheme will be developed to obtain long time solutions of the two dimensional equation. The possibility of metastable solutions will also be analyzed. The Cahn Hilliard equation models, among other phenomena, phase separation in binary alloys. The results of the research project will find applications in this and other related physical problems.