Article history: Received 26 February 2014 Received in revised form 20 August 2014 Accepted 26 August 2014 Available online 3 September 2014

Article history: Received 9 December 2010 Received in revised form 30 April 2011 Accepted 17 May 2011 Available online 27 May 2011

This paper is the third and last part of a work attempting to give a unified analysis of Discontinuous Galerkin methods. The purpose of this paper is to extend the framework that has been developed in part II for two-field Friedrichs’ systems associated with second-order PDE’s. We now consider two-field Friedrichs’ systems with partial L2-coercivity and three-field Friedrichs’ systems with an e...

We analyze existing discontinuous Galerkin methods on quasi-uniform meshes for singularly perturbed problems. We prove weighted L2 error estimates. We use the weighted estimates to prove L2 error estimates in regions where the solution is smooth. We also prove pointwise estimates in these regions.

We analyze existing discontinuous Galerkin methods on quasiuniform meshes for singularly perturbed problems. We prove weighted L2 error estimates. We use the weighted estimates to prove L2 error estimates in regions where the solution is smooth. We also prove pointwise estimates in these regions.

In this paper, an H-Galerkin mixed finite element method is discussed for the coupled Burgers equations. The optimal error estimates of the semi-discrete and fully discrete schemes of the coupled Burgers equation are derived. Keywords—The coupled Burgers equation; H-Galerkin mixed finite element method; Backward Euler’s method; Optimal error estimates.