Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



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
Published electronically: September 10, 2014
MathSciNet review: 3315503
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 65M12, 65M60, 35Q53

Retrieve articles in all journals with MSC (2010): 65M12, 65M60, 35Q53

Additional Information

Ohannes Karakashian
Affiliation: Department of Mathematics, The University of Tennessee, Knoxville, Tennessee 37996

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

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

American Mathematical Society