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Back and forth error compensation and correction methods for semi-lagrangian schemes with application to level set interface computations


Authors: Todd F. Dupont and Yingjie Liu
Journal: Math. Comp. 76 (2007), 647-668
MSC (2000): Primary 65M06, 65M12
DOI: https://doi.org/10.1090/S0025-5718-06-01898-9
Published electronically: October 30, 2006
MathSciNet review: 2291832
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Abstract: Semi-Lagrangian schemes have been explored by several authors recently for transport problems, in particular for moving interfaces using the level set method. We incorporate the backward error compensation method developed in our paper from 2003 into semi-Lagrangian schemes with almost the same simplicity and three times the complexity of a first order semi-Lagrangian scheme but with improved order of accuracy. Stability and accuracy results are proved for a constant coefficient linear hyperbolic equation. We apply this technique to the level set method for interface computation.


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Additional Information

Todd F. Dupont
Affiliation: Department of Computer Science, University of Chicago, Chicago, Illinois 60637
Email: dupont@cs.uchicago.edu

Yingjie Liu
Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
Email: yingjie@math.gatech.edu

DOI: https://doi.org/10.1090/S0025-5718-06-01898-9
Keywords: CIR scheme, front tracking, level set method, MacCormack scheme, semi-Lagrangian scheme.
Received by editor(s): February 1, 2005
Received by editor(s) in revised form: December 19, 2005
Published electronically: October 30, 2006
Additional Notes: The work of the first author was supported by the ASC Flash Center at the University of Chicago under DOE contract B532820, and by the MRSEC Program of the National Science Foundation under award DMR-0213745.
The work of the second author was supported by NSF grant DMS-0511815.
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.