In this paper we consider the local discontinuous Galerkin method based on the generalized alternating numerical fluxes, for solving the linear convection-diffusion equations in one dimension and two dimensions. As an application of generalized Gauss–Radau projections, we get rid of the dual argument and obtain directly the optimal L2-norm error estimate in a uniform framework. The sharpness of...

We consider some (anisotropic and piecewise constant) diffusion problems in domains of R, approximated by a discontinuous Galerkin method with polynomials of any degree. We propose an a posteriori error estimator based on gradient recovery by averaging. It is shown that this estimator gives rise to an upper bound where the constant is one up to some additional terms that guarantee reliability. ...

We consider linear first order scalar equations of the form ρt + div(ρv) + aρ = f with appropriate initial and boundary conditions. It is shown that approximate solutions computed using the discontinuous Galerkin method will converge in L[0, T ;L(Ω)] when the coefficients v and a and data f satisfy the minimal assumptions required to establish existence and uniqueness of solutions. In particula...

Article history: Received 22 July 2016 Received in revised form 18 September 2016 Accepted 3 October 2016 Available online 24 October 2016

Article history: Received 16 June 2014 Received in revised form 19 September 2014 Accepted 21 September 2014 Available online 8 October 2014

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In this paper, space-time discontinuous Galerkin finite element method for distributed optimal control problems governed by unsteady diffusion-convectionreaction equation without control constraints is studied. Time discretization is performed by discontinuous Galerkin method with piecewise constant and linear polynomials, while symmetric interior penalty Galerkin with upwinding is used for spa...

This paper is an attempt in seeking a connection between the discontinuous Petrov– Galerkin method of Demkowicz and Gopalakrishnan [13,15] and the popular discontinuous Galerkin method. Starting from a discontinuous Petrov–Galerkin (DPG) method with zero enriched order we re-derive a large class of discontinuous Galerkin (DG) methods for first order hyperbolic and elliptic equations. The first ...

We prove stability and derive error estimates for the recently introduced central discontinuous Galerkin method, in the context of linear hyperbolic equations with possibly discontinuous solutions. A comparison between the central discontinuous Galerkin method and the regular discontinuous Galerkin method in this context is also made. Numerical experiments are provided to validate the quantitat...