A Comparison of Semi-Lagrangian and Lagrange-Galerkin hp-FEM Methods in Convection-Diffusion Problems (Communications in Computational Physics, 2011)
We perform a comparison in terms of accuracy and CPU time between secondorder BDF semi-Lagrangian and Lagrange-Galerkin schemes in combination withhigh order finite element method. The numerical results show that for polynomialsof degree 2 semi-Lagrangian schemes are faster than Lagrange-Galerkin schemes forthe same number of degrees of freedom, however, for the same level of accuracy bothmethods are about the same in terms of CPU time. For polynomials of degree largerthan 2, Lagrange-Galerkin schemes behave better than semi-Lagrangian schemes interms of both accuracy and CPU time; specially, for polynomials of degree 8 or larger.Also, we have performed tests on the parallelization of these schemes and the speedupobtained is quasi-optimal even with more than 100 processors.