A posterior% error estimates are derived for a stabilized discontinuous Galerkin method (DGM) [l]. Equivalence between the error norm and the norm of the residual functional is proved, and consequently, global error estimates are obtained by estimating the norm of the residual. One-and two-dimensional numerical experiments are shown for a reaction-diffusion type model problem.

This paper is concerned with an interior penalty discontinuous Galerkin (IPDG) method based on a flexible type of non-polynomial local approximation space for the Helmholtz equation with varying wavenumber. The local approximation space consists of multiple polynomial-modulated phase functions which can be chosen according to the phase information of the solution. We obtain some approximation p...

We propose and analyze a hybrid discontinuous Galerkin method for the solution of incompressible flow problems, which allows to deal with pure Stokes, pure Darcy, and coupled Darcy-Stokes flow in a unified manner. The flexibility of the method is demonstrated in numerical examples.

in the recent paper, one of the numerical methods without element, for static analysis of thin plates displacement based on classical plates theory (cpt), has been presented. in this method, the domain of problem solving is shown only by the means of a set of nodes, and there is no need to any mesh scheme or element. one of the kinds of element free methods used here is the radial point interpo...

Article history: Received 11 April 2012 Received in revised form 17 July 2012 Accepted 31 August 2012 Available online 17 September 2012

We consider the numerical solution of an acoustic scattering problem by the Plane Wave Discontinuous Galerkin Method (PWDG) in the exterior of a bounded domain in R2. In order to apply the PWDG method, we introduce an artificial boundary to truncate the domain, and we impose a non-local Dirichlet-to-Neumann (DtN) boundary condition on the artificial curve. To define the method, we introduce new...

We describe the application of a local discontinuous Galerkin method to the numerical solution of the three-dimensional shallow water equations. The shallow water equations are used to model surface water flows where the hydrostatic pressure assumption is valid. The authors recently developed a DGmethod for the depth-integrated shallow water equations. The method described here is an extension ...

We present in this paper a new a posteriori error estimator for the Baumann-Oden version of the Discontinuous Galerkin Method. The error estimator is based on the residual of the partial differential equation. In the case of the reaction-diffusion equation, the norm of the residual is shown to be equivalent to the error in some specific energy-type norms. We propose here a method to efficiently...

We develop a high-order positivity-preserving discontinuous Galerkin (DG) scheme for linear Vlasov-Boltzmann transport equations (Vlasov-BTE) under the action of quadratically confined electrostatic potentials. The solutions of such BTEs are positive probability distribution functions and it is very challenging to have a mass-conservative, high-order accurate scheme that preserves positivity of...

We prove local and pointwise error estimates for the local discontinuous Galerkin method applied to the Stokes problem in two and three dimensions. By using techniques originally developed by A. Schatz [Math. Comp., 67 (1998), 877-899] to prove pointwise estimates for the Laplace equation, we prove optimal weighted pointwise estimates for both the velocity and the pressure for domains with smoo...