This workshop will survey novel discretization techniques in numerical partial differential equations that address the computational challenges posed by higher dimensions, higher orders, complex spaces, complex geometries, nonlinearities and multiscales. The focus is on new and fundamental methodologies that impact diverse areas of numerical partial differential equations. Topics include discontinuous Galerkin methods, finite element exterior calculus, higher order methods, isogeometric analysis, mimetic finite difference methods, multiscale methods, reduced basis methods, sparse grids, and others.