Research Details

 

Applied Math Modeling


My work in this area focusses on partial differential equation models for physical systems arising in continuum mechanics.  I am particularly interested in asymptotics and simulation for higher-order PDEs and especially in finite time blow-up phenomena.  Lately, I have also begun working on problems from image processing.


Numerical Analysis


The PDEs I typically study require adaptive numerical methods in time and space.  This has lead to work on Parabolic Monge-Ampere equations, r-adaptivity and scaling invariance.