In this paper, we study the local discontinuous Galerkin (LDG) finite element method for solving a nonlinear Burger’s equation with Dirichlet boundary conditions. Based on the Hopf–Cole transformation, we transform the original problem into a linear heat equation with Neumann boundary conditions. The heat equation is then solved by the LDG finite element method with special chosen numerical flu...

We propose a multilevel preconditioning strategy for the iterative solution of large sparse linear systems arising from a nite element discretization of the radiation di usion equations. In particular, these equations are solved using a mixed nite element scheme in order to make the discretization discontinuous, which is imposed by the application in which the di usion equation will be embedded...

Recently, we have proposed a method for solving steady-state convection-diffusion equations, including the full compressible Navier-Stokes equations [17]. The method is a combination of a mixed Finite Element method for the diffusion terms, and a Discontinuous Galerkin method for the convection term. The method is fully implicit, and the globally coupled unknowns are the hybrid variables, i.e.,...

We present a two-scale finite element method for solving Brinkman’s equations with piece-wise constant coefficients. This system of equations model fluid flows in highly porous, heterogeneous media with complex topology of the heterogeneities. We make use of the recently proposed discontinuous Galerkin FEM for Stokes equations by Wang and Ye in [12] and the concept of subgrid approximation deve...

Abstract. Many physical materials of practical relevance can attain several variants of crystalline microstructure. The appropriate energy functional is necessarily non-convex, and the minimization of the functional becomes a challenging problem. A new numerical method based on discontinuous nite elements and a scaled energy functional is proposed. It exhibits excellent convergence behavior for...

A detailed a priori error estimate is provided for a continuous-discontinuous Galerkin finite element method for the generalized 2D vorticity dynamics equations which describe several types of geophysical flows, including the Euler equations. The algorithm consists of a continuous Galerkin finite element method for the stream function and a discontinous Galerkin finite element method for the (p...

We develop a Hamiltonian discontinuous finite element discretization of a generalized Hamiltonian system for linear hyperbolic systems, which includes the rotating shallow water equations, the acoustic and Maxwell equations. These equations have a Hamiltonian structure with a bilinear Poisson bracket, and as a consequence the phase-space structure, mass and energy are preserved. We discretize t...

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...

In this paper we establish a best approximation property of fully discrete Galerkin finite element solutions of second order parabolic problems on convex polygonal and polyhedral domains in the L∞ norm. The discretization method uses of continuous Lagrange finite elements in space and discontinuous Galerkin methods in time of an arbitrary order. The method of proof differs from the established ...