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A posteriori error estimates for discontinuous Galerkin methods for the generalized Korteweg-de Vries equation


Authors: Ohannes Karakashian and Charalambos Makridakis
Journal: Math. Comp. 84 (2015), 1145-1167
MSC (2010): Primary 65M12, 65M60; Secondary 35Q53
DOI: https://doi.org/10.1090/S0025-5718-2014-02878-0
Published electronically: September 10, 2014
MathSciNet review: 3315503
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Abstract: We construct, analyze and numerically validate a posteriori error estimates for conservative discontinuous Galerkin (DG) schemes for the Generalized Korteweg-de Vries (GKdV) equation. We develop the concept of dispersive reconstruction, i.e., a piecewise polynomial function which satisfies the GKdV equation in the strong sense but with a computable forcing term enabling the use of a priori error estimation techniques to obtain computable upper bounds for the error. Both semidiscrete and fully discrete approximations are treated.


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Additional Information

Ohannes Karakashian
Affiliation: Department of Mathematics, The University of Tennessee, Knoxville, Tennessee 37996
Email: ohannes@math.utk.edu

Charalambos Makridakis
Affiliation: Department of Applied Mathematics, The University of Crete, Heraklion, Greece – and – IACM-FORTH, 70013 Heraklion-Crete, Greece
Address at time of publication: School of Mathematical and Physical Sciences, University of Sussex, Brighton, BN1 9QH, United Kingdom
Email: makr@tem.uoc.gr

DOI: https://doi.org/10.1090/S0025-5718-2014-02878-0
Received by editor(s): February 5, 2013
Received by editor(s) in revised form: August 8, 2013
Published electronically: September 10, 2014
Additional Notes: The work of the first author was partially supported by NSF grants DMS-0811314 and NSF-1216740
The work of the second author was supported by EU program FP7-REGPOT-2009-1, grant 245749 through the Archimedes Center for Modeling, Analysis and Computation (ACMAC) of the Department of Applied Mathematics at the University of Crete and by GSRT grant 1456.
Article copyright: © Copyright 2014 American Mathematical Society