PhD studentship on Numerical methods for higher-order nonlinear partial differential equations
Deadline: 1 sep 2016
We are pleased to offer this fully-funded PhD studentship, available in the Department of Mathematics at the University of Sussex, supported by the Leverhulme Trust research project grant "Novel discretisations of higher-order nonlinear PDE" (RPG-2015-069).
The project aims to derive, implement and analyse numerical schemes for higher-order nonlinear partial differential equations (PDE).
Higher-order nonlinear PDE have emerged as a hot topic in mathematical research and practical applications alike in recent years, driven by modern applications and by the curiosity for a better understanding of their mathematical properties. The geometric interpretation of a large class of these equations as gradient flows has opened a radically new viewpoint on these problems, and allowed for a major breakthrough in their analysis, with exciting and unexpected results. In this project we seek to use this geometric, gradient flow approach as a novel framework for the development of numerical schemes which preserve the equations' special structure at the discrete level.
The project will be supervised by Dr Bertram Düring.