We explore two problems with applications in detonation shock dynamics and molecular dynamics. First, we discuss level set methods, which are a popular approach to modeling evolving interfaces. We present a level set advection solver in two and three dimensions using high-order finite elements. Our approach leads to stable front propagation and convergence on high-order, curved, unstructured meshes. The solver's ability to implicitly track moving fronts lends itself to a number of applications; in particular, we highlight applications to high-explosive (HE) burn and detonation shock dynamics (DSD). In the second half, we look at molecular dynamics (MD) simulations, which are widely used to study the motion and thermodynamic properties of molecules. Computational limitations and the complexity of problems, however, result in the need for error quantification. We examine the inherent two-scale nature of MD to construct a large-scale dynamics approximation as a means of error estimation.