Research
Areas of Interest
Numerical methods for parabolic PDE and interace problems
- diffuse interface approximation methods
- DG and finite element methods
- energy/entropy stable methods
- positivity preserving methods
- adaptive mesh refinement
- multigrid methods/fast solvers
Complex fluids
- interfaces
- multiphase flows
- phase transitions
- non-isothermal models
- thermodynamically consistent models
- polymeric flows
- kinetic equations
Nonlinear PDE
- properties of solutions
- singular perturbation problems
- asymptotic methods
- Gamma convergence
- existence, uniqueness, and regularity
Biological growth
- developmental biology
- spatio-temporal cancer progression models
- membrane dynamics
Materials science
- ionic materials
- phase field and phase field crystal (PFC) methods
- crystalization
- material anisotropy
- structural phase transistions