Peszynska's research interests and accomplishments are in mathematical and computational modeling of of flow and transport in porous media and other phenomena of similar character described by nonlinear coupled PDEs with highly heterogeneous and multiscale data. She is interested in analysis of solutions as well as in development and analysis of numerical algorithms. Most recently she has worked on adaptive techniques for coupled, multiscale, and nonlocal models. In addition, she has been involved in various high-performance computing projects involving domain decomposition, parallel computing, and data-intensive grid-based simulations and visualization.
Currently, she is involved in two funded projects: Model Adaptivity for Porous Media and Multiscale Mathematics Research Group.