- Partial Differential Equations (PDEs) related to fluids and moving boundaries
- Free boundary and geometric evolution problems
- Numerical analysis and finite element methods (FEM)
- Mesh generation
- Optimal control of PDEs and shape optimization
My research focuses on the numerical analysis and simulation of physics on a computer. Much of my work is on free boundary/moving interface problems where geometry plays a critical role. Examples are two-phase fluid flows and elastic boundaries that couple to other physics, such as electric fields. I also work on optimal shape design problems (optimal control) with PDE-constraints. The main aspects of my work are mathematical modeling, PDE theory, and FEM.