Yi's general research interest is in the area of numerical analysis, including the mathematical and computational modeling of problems motivated by physical processes and phenomena in fluid mechanics and material science and the analysis and implementation of the resulting numerical methods. Her recent work has been focused on Mixed Finite Element Methods for Linear Elasticity and Eulerian-Lagrangian Finite Element Methods for Convection-Diffusion problems. Currently, she is working on multiscale fluid flow problems in porous media.