A Comparison of Semi-Lagrangian and Lagrange-Galerkin <em>hp</em>-FEM Methods in Convection-Diffusion Problems
Year: 2011
Communications in Computational Physics, Vol. 9 (2011), Iss. 4 : pp. 1020–1039
Abstract
We perform a comparison in terms of accuracy and CPU time between second order BDF semi-Lagrangian and Lagrange-Galerkin schemes in combination with high order finite element method. The numerical results show that for polynomials of degree 2 semi-Lagrangian schemes are faster than Lagrange-Galerkin schemes for the same number of degrees of freedom, however, for the same level of accuracy both methods are about the same in terms of CPU time. For polynomials of degree larger than 2, Lagrange-Galerkin schemes behave better than semi-Lagrangian schemes in terms 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 speedup obtained is quasi-optimal even with more than 100 processors.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.041209.160910a
Communications in Computational Physics, Vol. 9 (2011), Iss. 4 : pp. 1020–1039
Published online: 2011-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20