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Volume 9, Issue 4
A Comparison of Semi-Lagrangian and Lagrange-Galerkin hp-FEM Methods in Convection-Diffusion Problems

Pedro Galán del Sastre & Rodolfo Bermejo

DOI: 10.4208/cicp.041209.160910a

Commun. Comput. Phys., 9 (2011), pp. 1020-1039.

Published online: 2011-09

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  • 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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@Article{CiCP-9-1020, author = {Pedro Galán del Sastre and Rodolfo Bermejo}, title = {A Comparison of Semi-Lagrangian and Lagrange-Galerkin hp-FEM Methods in Convection-Diffusion Problems}, journal = {Communications in Computational Physics}, year = {2011}, volume = {9}, number = {4}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.041209.160910a}, url = {http://global-sci.org/intro/article_detail/cicp/7533.html} }
TY - JOUR T1 - A Comparison of Semi-Lagrangian and Lagrange-Galerkin hp-FEM Methods in Convection-Diffusion Problems AU - Pedro Galán del Sastre & Rodolfo Bermejo JO - Communications in Computational Physics VL - 4 SP - 1020 EP - 1039 PY - 2011 DA - 2011/09 SN - 9 DO - http://doi.org/10.4208/cicp.041209.160910a UR - https://global-sci.org/intro/article_detail/cicp/7533.html KW - AB -

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.

Pedro Galán del Sastre and Rodolfo Bermejo. (2011). A Comparison of Semi-Lagrangian and Lagrange-Galerkin hp-FEM Methods in Convection-Diffusion Problems. Communications in Computational Physics. 9 (4). 1020-1039. doi:10.4208/cicp.041209.160910a
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