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Research Interests

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.

This material is based upon work supported by the National Science Foundation under Grant No. 1115636, 1418994.