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A limiting strategy for the back and forth error compensation and correction method for solving advection equations


Authors: Lili Hu, Yao Li and Yingjie Liu
Journal: Math. Comp. 85 (2016), 1263-1280
MSC (2010): Primary 65M06, 65M12
Published electronically: January 13, 2016
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Abstract: We further study the properties of the back and forth error compensation and correction (BFECC) method for advection equations such as those related to the level set method and for solving Hamilton-Jacobi equations on unstructured meshes. In particular, we develop a new limiting strategy which requires another backward advection in time so that overshoots/
undershoots on the new time level get exposed when they are transformed back to compare with the solution on the old time level. This new technique is very simple to implement even for unstructured meshes and is able to eliminate artifacts induced by jump discontinuities in derivatives of the solution as well as by jump discontinuities in the solution itself (even if the solution has large gradients in the vicinities of a jump). Typically, a formal second order method for solving a time dependent Hamilton-Jacobi equation requires quadratic interpolation in space. A BFECC method on the other hand only requires linear interpolation in each step, thus is local and easy to implement even for unstructured meshes.


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Additional Information

Lili Hu
Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
Email: lhu33@math.gatech.edu

Yao Li
Affiliation: Courant Institute of Mathematics, New York University, New York
Email: yaoli@cims.nyu.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/mcom/3026
Received by editor(s): April 11, 2013
Received by editor(s) in revised form: April 22, 2014
Published electronically: January 13, 2016
Additional Notes: The first author’s research was supported in part by NSF grant DMS-1115671
The third author’s research was supported in part by NSF grant DMS-1115671
Article copyright: © Copyright 2016 American Mathematical Society