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A Comparison of Semi-Lagrangian and Lagrange-Galerkin hp-FEM Methods in Convection-Diffusion Problems

Published online by Cambridge University Press:  20 August 2015

Pedro Galán del Sastre  and
Rodolfo Bermejo
Pedro Galán del Sastre*
Affiliation:
Departamento de Matemática Aplicada al Urbanismo, a la Edificación y al Medio Ambiente, E.T.S.A.M., Universidad Politécnica de Madrid, Avda. Juan de Herrera 4, 28040 Madrid, Spain
Rodolfo Bermejo*
Affiliation:
Departamento de Matematica Aplicada, E.T.S.I.I., Universidad Politécnica de Madrid, C/ José Gutiérrez Abascal 2, 28006 Madrid, Spain
*
Corresponding author.Email:pedro.galan@upm.es
Email:rbermejo@etsii.upm.es
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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.

Keywords

65M6065L6065N3065M2576M1076M25Navier-Stokes equationsconvection-diffusion equationssemi-LagrangianLagrange-Galerkinsecond order backward difference formulahp-finite element method
Type
Research Article
Information
Communications in Computational Physics , Volume 9 , Issue 4 , April 2011 , pp. 1020 - 1039
Copyright
Copyright © Global Science Press Limited 2011

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