Space-time spectral element methods for unsteady convection-diffusion problems

Deals with the formulation and application of temporal and spatial spectral element approximations for the solution of convection-diffusion problems. Proposes a new high-order splitting space-time spectral element method which exploits space-time discontinuous Galerkin for the first hyperbolic substep and space continuous-time discontinuous Galerkin for the second parabolic substep. Analyses this method and presents its characteristics in terms of accuracy and stability. Also investigates a subcycling technique, in which several hyperbolic substeps are taken for each parabolic substep; a technique which enables fast, cost-effective time integration with little loss of accuracy. Demonstrates, by a numerical comparison with other coupled and splitting space-time spectral element methods, that the proposed method exhibits significant improvements in accuracy, stability and computational efficiency, which suggests that this method is a potential alternative to existing schemes. Describes several areas for future research.