Research

My research lies at the intersection of Numerical Analysis and Partial Differential Equations (PDEs). In particular I use the finite element method (FEM) to generate approximate solutions of PDEs and analyze the qualitative behavior of the solutions.

Currently, I am working on a three-dimensional elliptic equation and the Green's function associated with the problem. Green's functions often play a critical role in FEM analysis as a tool in establishing convergence of solutions, regularity of solutions, an optimal control problems.

My work stems from work by my advisor Dr. Dmitriy Leykekhman. In a 2014 paper Leykekhman and Pruitt established a two-dimensional Harnack type inequality for the discrete solution to Laplace's problem. In three-dimensions the same results does not seems to hold due to the structure of the finite element discretization. Additionally, I am investigating comparisons of the discrete Green's function and the continuous Green's function.

I am also broadly interested in the scholarship of teaching and learning. In particular, studying the effectiveness of active learning strategies and engagement of students in the classroom.

I have previously written articles for UConn That Wasn't on the Syllabus blog:

Applying James Lang's Small Teaching in STEM Classrooms

Building Classroom Dialogue using Webb's Depth of Knowledge