Ljp. Timmermans et al., TAYLOR-GALERKIN-BASED SPECTRAL ELEMENT METHODS FOR CONVECTION-DIFFUSION PROBLEMS, International journal for numerical methods in fluids, 18(9), 1994, pp. 853-870
Several explicit Taylor Galerkin-based time integration schemes are pr
oposed for the solution of both linear and non-linear convection probl
ems with divergence-free velocity. These schemes are based on second-o
rder Taylor series of the time derivative. The spatial discretization
is performed by a high-order Galerkin spectral element method. For con
vection-diffusion problems an operator-splitting technique is given th
at decouples the treatment of the convective and diffusive terms. Both
problems are then solved using a suitable time scheme. The Taylor Gal
erkin methods and the operator-splitting scheme are tested numerically
for both convection and convection diffusion problems.