My research program lies at the intersection of mathematics, physics, and computation, and involves working in the areas of numerical analysis, applied analysis, partial differential equations (PDE), and mathematical physics.  My main area of expertise is the analysis and numerical treatment of PDE, with a particular focus on nonlinear geometric PDE and adaptive numerical methods.  My research projects typically center around developing mathematical theorems (for analyzing nonlinear PDE and developing approximation theory) and mathematical algorithms (for efficient and reliable numerical solution of nonlinear PDE problems).  Although my current focus is on mathematical and numerical general relativity in astrophysics, the same general types of mathematical problems arise in nearly every area of science and engineering, and I continue to be involved in long-term projects in other fields such as biophysics, biochemistry, and engineering.  In addition to my journal publications, I am the coauthor of a graduate textbook on applied analysis and PDE with Ivar Stakgold.