An hp-local Discontinuous Galerkin Method for Parabolic Integro-Differential Equations

Handle URI:
http://hdl.handle.net/10754/597526
Title:
An hp-local Discontinuous Galerkin Method for Parabolic Integro-Differential Equations
Authors:
Pani, Amiya K.; Yadav, Sangita
Abstract:
In this article, a priori error bounds are derived for an hp-local discontinuous Galerkin (LDG) approximation to a parabolic integro-differential equation. It is shown that error estimates in L 2-norm of the gradient as well as of the potential are optimal in the discretizing parameter h and suboptimal in the degree of polynomial p. Due to the presence of the integral term, an introduction of an expanded mixed type Ritz-Volterra projection helps us to achieve optimal estimates. Further, it is observed that a negative norm estimate of the gradient plays a crucial role in our convergence analysis. As in the elliptic case, similar results on order of convergence are established for the semidiscrete method after suitably modifying the numerical fluxes. The optimality of these theoretical results is tested in a series of numerical experiments on two dimensional domains. © 2010 Springer Science+Business Media, LLC.
Citation:
Pani AK, Yadav S (2010) An hp-local Discontinuous Galerkin Method for Parabolic Integro-Differential Equations. Journal of Scientific Computing 46: 71–99. Available: http://dx.doi.org/10.1007/s10915-010-9384-z.
Publisher:
Springer Nature
Journal:
Journal of Scientific Computing
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
6-Jun-2010
DOI:
10.1007/s10915-010-9384-z
Type:
Article
ISSN:
0885-7474; 1573-7691
Sponsors:
The authors gratefully acknowledge the research support of the Department of Science and Technology, Government of India through project No. 08DST012. They also acknowledge Professor Neela Nataraj for her valuable suggestions and help on the numerical experiments. This publication is also based on work supported in part by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). Further, the authors thank both the referees for their valuable comments and suggestions.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorPani, Amiya K.en
dc.contributor.authorYadav, Sangitaen
dc.date.accessioned2016-02-25T12:41:27Zen
dc.date.available2016-02-25T12:41:27Zen
dc.date.issued2010-06-06en
dc.identifier.citationPani AK, Yadav S (2010) An hp-local Discontinuous Galerkin Method for Parabolic Integro-Differential Equations. Journal of Scientific Computing 46: 71–99. Available: http://dx.doi.org/10.1007/s10915-010-9384-z.en
dc.identifier.issn0885-7474en
dc.identifier.issn1573-7691en
dc.identifier.doi10.1007/s10915-010-9384-zen
dc.identifier.urihttp://hdl.handle.net/10754/597526en
dc.description.abstractIn this article, a priori error bounds are derived for an hp-local discontinuous Galerkin (LDG) approximation to a parabolic integro-differential equation. It is shown that error estimates in L 2-norm of the gradient as well as of the potential are optimal in the discretizing parameter h and suboptimal in the degree of polynomial p. Due to the presence of the integral term, an introduction of an expanded mixed type Ritz-Volterra projection helps us to achieve optimal estimates. Further, it is observed that a negative norm estimate of the gradient plays a crucial role in our convergence analysis. As in the elliptic case, similar results on order of convergence are established for the semidiscrete method after suitably modifying the numerical fluxes. The optimality of these theoretical results is tested in a series of numerical experiments on two dimensional domains. © 2010 Springer Science+Business Media, LLC.en
dc.description.sponsorshipThe authors gratefully acknowledge the research support of the Department of Science and Technology, Government of India through project No. 08DST012. They also acknowledge Professor Neela Nataraj for her valuable suggestions and help on the numerical experiments. This publication is also based on work supported in part by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). Further, the authors thank both the referees for their valuable comments and suggestions.en
dc.publisherSpringer Natureen
dc.subjectLDG methoden
dc.subjectMixed type Ritz-Volterra projectionen
dc.subjectNegative norm estimatesen
dc.subjectOptimal error boundsen
dc.subjectParabolic integro-differential equationen
dc.subjectRole of stabilizing parametersen
dc.subjectSemidiscreteen
dc.titleAn hp-local Discontinuous Galerkin Method for Parabolic Integro-Differential Equationsen
dc.typeArticleen
dc.identifier.journalJournal of Scientific Computingen
dc.contributor.institutionIndian Institute of Technology, Bombay, Mumbai, Indiaen
kaust.grant.numberKUK-C1-013-04en
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