Welcome to the homepage for the Mathematical Modeling and Computational Physics (MMCP) Laboratory! We are led by Dr. David M. Williams, an assistant professor in the mechanical engineering department at Pennsylvania State University. We specialize in the development of modern, high-order, robust, massively-parallel, computational algorithms for multi-physics problems involving fluid dynamics, structural mechanics, acoustics, chemical reactions, and heat transfer.  In particular, we are most interested in developing and improving finite element methods for solving nonlinear partial differential equations in two-, three- and four-dimensional space. We favor finite element methods over finite difference or finite volume methods due to: 1) their inherent ability to operate on unstructured, non-conforming meshes, 2) their straightforward extension to high-order accuracy while maintaining a compact stencil, and 3) their elegant mathematical foundation.