Spectral element approximation of convection–diffusion type problems Original Research Article

A spectral element implementation of the discontinuous Galerkin method is examined for convection–diffusion type problems. The computational domain is subdivided into non-overlapping subdomains, and a high order, Legendre polynomial approximation is constructed on each subdomain. A variational formulation is used, and the flux across the subdomain interfaces is approximated using a van Leer flux splitting scheme for the convective terms and a penalty type method for the viscous terms.