Volume 28, Issue 4
Equivalence of Semi-Lagrangian and Lagrange-Galerkin Schemes Under Constant Advection Speed

Roberto Ferretti

J. Comp. Math., 28 (2010), pp. 461-473.

Published online: 2010-08

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  • Abstract

We compare in this paper two major implementations of large time-step schemes for advection equations, i.e., Semi-Lagrangian and Lagrange-Galerkin techniques. We show that SL schemes are equivalent to exact LG schemes via a suitable definition of the basis functions. In this paper, this equivalence will be proved assuming some simplifying hypotheses, mainly constant advection speed, uniform space grid, symmetry and translation invariance of the cardinal basis functions for interpolation. As a byproduct of this equivalence, we obtain a simpler proof of stability for SL schemes in the constant-coefficient case.

  • Keywords

Semi-Lagrangian schemes, Lagrange-Galerkin schemes, Stability.

  • AMS Subject Headings

65N12, 65M10, 49L25.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-28-461, author = {}, title = {Equivalence of Semi-Lagrangian and Lagrange-Galerkin Schemes Under Constant Advection Speed}, journal = {Journal of Computational Mathematics}, year = {2010}, volume = {28}, number = {4}, pages = {461--473}, abstract = {

We compare in this paper two major implementations of large time-step schemes for advection equations, i.e., Semi-Lagrangian and Lagrange-Galerkin techniques. We show that SL schemes are equivalent to exact LG schemes via a suitable definition of the basis functions. In this paper, this equivalence will be proved assuming some simplifying hypotheses, mainly constant advection speed, uniform space grid, symmetry and translation invariance of the cardinal basis functions for interpolation. As a byproduct of this equivalence, we obtain a simpler proof of stability for SL schemes in the constant-coefficient case.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1003-m0012}, url = {http://global-sci.org/intro/article_detail/jcm/8532.html} }
TY - JOUR T1 - Equivalence of Semi-Lagrangian and Lagrange-Galerkin Schemes Under Constant Advection Speed JO - Journal of Computational Mathematics VL - 4 SP - 461 EP - 473 PY - 2010 DA - 2010/08 SN - 28 DO - http://doi.org/10.4208/jcm.1003-m0012 UR - https://global-sci.org/intro/article_detail/jcm/8532.html KW - Semi-Lagrangian schemes, Lagrange-Galerkin schemes, Stability. AB -

We compare in this paper two major implementations of large time-step schemes for advection equations, i.e., Semi-Lagrangian and Lagrange-Galerkin techniques. We show that SL schemes are equivalent to exact LG schemes via a suitable definition of the basis functions. In this paper, this equivalence will be proved assuming some simplifying hypotheses, mainly constant advection speed, uniform space grid, symmetry and translation invariance of the cardinal basis functions for interpolation. As a byproduct of this equivalence, we obtain a simpler proof of stability for SL schemes in the constant-coefficient case.

Roberto Ferretti. (2019). Equivalence of Semi-Lagrangian and Lagrange-Galerkin Schemes Under Constant Advection Speed. Journal of Computational Mathematics. 28 (4). 461-473. doi:10.4208/jcm.1003-m0012
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