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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, 1555222 (CAREER).