Galerkin methods are ubiquitous in the later-undergraduate/postgraduate curriculum as a fundamental method to obtain existence and uniqueness of weak solutions to linear PDE. There are important cases where the Galerkin method can be adapted to give remarkable results. In particular, nonlinear problems have been approached via the Galerkin method for decades.
This project is concerned with examining new nonlinear Galerkin methods and identifying stand-out cases where the new innovations yield results not easily obtainable by other more standard methods techniques.
University of Wollongong
Dean is starting his third year in a Bachelor of Mathematics Advanced at the University of Wollongong. Currently Dean’s interests are in pure mathematics, more specifically analysis and PDE theory. Dean intends on completing his honours in 2021.