We prove optimal convergence rates for the approximation provided by the original discontinuous Galerkin method for the transport-reaction problem. This is achieved in any dimension on meshes related in a suitable way to the possibly variable velocity carrying out the transport. Thus, if the method uses polynomials of degree k, the L2-norm of the error is of order k + 1. Moreover, we also show that, by means of an element-by-element postprocessing, a new approximate flux can be obtained which superconverges with order k + 1.
- Convection-reaction equation
- Discontinuous Galerkin methods
- Error estimates