SPACE-TIME SPECTRAL ELEMENT METHODS FOR UNSTEADY CONVECTION-DIFFUSIONPROBLEMS

Deals with the formulation and application of temporal and spatial spe ctral element approximations for the solution of convection-diffusion problems. Proposes a new high-order splitting space-time spectral elem ent method which exploits space-time discontinuous Galerkin for the fi rst hyperbolic substep and space continuous-time discontinuous Galerki n for the second parabolic substep. Analyses this method and presents its characteristics in terms of accuracy and stability. Also investiga tes a subcycling technique, in which several hyperbolic substeps are t aken 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 significa nt improvements in accuracy, stability and computational efficiency, w hich suggests that this method is a potential alternative to existing schemes. Describes several areas for future research.