A SPECTRAL LAGRANGE-GALERKIN METHOD FOR CONVECTION-DOMINATED DIFFUSION-PROBLEMS

The spectral Lagrange-Galerkin method is a numerical technique for tim e-dependent convection-diffusion problems based on combining a Lagrang ian formulation of the equations with the spectral method. The resulti ng scheme can be shown to be unconditionally stable for linear advecti on-diffusion equations, and optimal convergence rates may be obtained. Both the spectral accuracy and the efficiency of the scheme are exami ned theoretically and by various numerical experiments, and extensions of the method to give high accuracy in time are presented.