Numerical analysis and partial differential equations; the construction, analysis, and implementation of numerical approximation techniques (specifically, the finite element method) to nonlinear partial differential equations; in particular:
- Non-Newtonian fluids; modeling and numerical simulation
- Phase field methods and the dynamics for parabolic partial differential equations, in particular the Cahn-Hilliard equation
- Adaptive finite element algorithms and a-posteriori error control
- Discontinuous finite element methods
A
summary of the problem which motivated part of my current research is available.
