The paper is concerned with the discontinuous Galerkin finite element method for the numerical solution of nonlinear conservation laws and nonlinear convection-diffusion problems with emphasis on applications to the simulation of compressible flows. We discuss two versions of this method: (a) Finite volume discontinuous Galerkin method, which is a generalization of the combined finite volume—fi...

A method for calculating special grid placement for three-point schemes which yields exponential superconvergence of the Neumann to Dirichlet map has been suggested earlier. Here we show that such a grid placement can yield impedance which is equivalent to that of a spectral Galerkin method, or more generally to that of a spectral Galerkin-Petrov method. In fact we show that for every stable Ga...

Abstract. We present and analyze a subgrid viscosity Lagrange-Galerkin method that combines the subgrid eddy viscosity method proposed in W. Layton, A connection between subgrid scale eddy viscosity and mixed methods. Appl. Math. Comp., 133: 147-157, 2002, and a conventional Lagrange-Galerkin method in the framework of P1⊕ cubic bubble finite elements. This results in an efficient and easy to i...

A space-time Galerkin/least-squares finite element method was presented in [l] for numerical simulation of single-carrier hydrodynamic semiconductor device equations. The single-carrier hydrodynamic device equations were shown to resemble the ideal gas equations and Galerkin/least-squares finite element method, originally developed for computational fluid dynamics equations [16], was extended t...