An Optimal-Order Error Estimate for the Discontinuous Galerkin Method

An Optimal-Order Error Estimate for the Discontinuous Galerkin Method

In this paper a new approach is developed for analyzing the discontinuous Galerkin method for hyperbolic equations. For a model problem in R2, the method is shown to converge at a rate 0(hn+l) when applied with nth degree polynomial approximations over a semiuniform triangulation, assuming sufficient regularity in the solution.

An Optimal Estimate for the Local Discontinuous Galerkin Method

L2 error estimates for the Local Discontinuous Galerkin (LDG) method have been theoretically proven for linear convection diffusion problems and periodic boundary conditions. It has been proven that when polynomials of degree k are used, the LDG method has a suboptimal order of convergence k. However, numerical experiments show that under a suitable choice of the numerical flux, higher order of...

Optimal Error Estimates of the Semidiscrete Local Discontinuous Galerkin Methods for High Order Wave Equations

In this paper, we introduce a general approach for proving optimal L2 error estimates for the semi-discrete local discontinuous Galerkin (LDG) methods solving linear high order wave equations. The optimal order of error estimates hold not only for the solution itself but also for the auxiliary variables in the LDG method approximating the various order derivatives of the solution. Several examp...

High-Order Discontinuous Galerkin Method on Hexahedral Elements for Aeroacoustics High-Order Discontinuous Galerkin Method on Hexahedral Elements for Aeroacoustics

Local error analysis of the interior penalty discontinuous Galerkin method for second order elliptic problems

A local a priori and a posteriori analysis is developed for the Galerkin method with discontinuous finite elements for solving stationary diffusion problems. The main results are an optimal-order estimate for the point-wise error and a corresponding a posteriori error bound. The proofs are based on weighted -norm error estimates for discrete Green functions as already known for the ‘continuous’...