A. Ware, A SPECTRAL LAGRANGE-GALERKIN METHOD FOR CONVECTION-DOMINATED DIFFUSION-PROBLEMS, Computer methods in applied mechanics and engineering, 116(1-4), 1994, pp. 227-234
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.