Computer Methods in Applied Mechanics and Engineering
Discontinuous functions, Galerkin methods, Transport theory -- Mathematics, Finite element method
Considering a simple model transport problem, we present a new finite element method. While the new method fits in the class of discontinuous Galerkin (DG) methods, it differs from standard DG and streamline diffusion methods, in that it uses a space of discontinuous trial functions tailored for stability. The new method, unlike the older approaches, yields optimal estimates for the primal variable in both the element size h and polynomial degree p, and outperforms the standard upwind DG method.
Demkowicz, Leszek and Gopalakrishnan, Jay, "A Class of Discontinuous Petrov–Galerkin Methods. Part I: The Transport Equation" (2010). Mathematics and Statistics Faculty Publications and Presentations. 55.