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

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 L2 t (L2 x) 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 rate of the various error indicators on a model problem. Key words: a posteriori error estimates, duality techniques, non-symmetric interior penalty, local discontinuous Galerkin, convection-diffusion equations

• Type: Journal
• Year: 2005
• Where: APPML
• Authors: Alexandre Ern, Jennifer Proft
• Keywords: APPML 2005, Local Discontinuous Galerkin, Non-symmetric Interior Penalty, Posteriori Error