A posteriori discontinuous Galerkin error estimates for transient convection–diffusion equations

Abstract

A posteriori error estimates are derived for unsteady convection–diffusion equations discretized with the non-symmetric interior penalty and the local discontinuous Galerkin methods. First, an error representation formula in a user specified output functional is derived using duality techniques. Then, an L t 2 ( L x 2 ) a posteriori estimate consisting of elementwise residual-based error indicators is obtained by eliminating the dual solution. Numerical experiments are performed to assess the convergence rates of the various error indicators on a model problem.