Goal-oriented error analysis of a DG scheme for a second gradient elastodynamics model

Jan Giesselmann; Tristan Pryer

doi:10.1007/978-3-319-57397-7_39

Goal-oriented error analysis of a DG scheme for a second gradient elastodynamics model

Research output: Chapter or section in a book/report/conference proceeding › Chapter in a published conference proceeding

Abstract

In this note we propose a discontinuous Galerkin in space, continuous Galerkin in time method for a problem arising in elastodynamics with phase transition. We make use of a dispersion operator from (Bona et al., Math. Comput. 82(283), 1401–1432, 2013) [3] allowing us to construct a consistent scheme. We derive goal-oriented a posteriori error estimators for this scheme based on dual weighted residuals. We conclude by summarising extensive numerical experiments.

Original language	English
Title of host publication	Finite Volumes for Complex Applications VIII—Methods and Theoretical Aspects - FVCA8 2017
Editors	Clement Cances, Pascal Omnes
Publisher	Springer New York
Pages	457-466
Number of pages	10
ISBN (Print)	9783319573960
DOIs	https://doi.org/10.1007/978-3-319-57397-7_39
Publication status	Published - 24 May 2017
Event	8th International Symposium on Finite Volumes for Complex Applications - Methods and Theoretical Aspects, FVCA8 2017 - Lille, France Duration: 12 Jun 2017 → 16 Jun 2017

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	199
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	8th International Symposium on Finite Volumes for Complex Applications - Methods and Theoretical Aspects, FVCA8 2017
Country/Territory	France
City	Lille
Period	12/06/17 → 16/06/17

Bibliographical note

Funding Information:
T.P. gratefully acknowledges support of the EPSRC grant EP/P000835/1. J.G. gratefully acknowledges support of the Baden-Württemberg fundation for the project “Numerical Methods for Multi-Phase Flows with Strongly Varying Mach Numbers”.

Publisher Copyright:
© Springer International Publishing AG 2017.

Funding

T.P. gratefully acknowledges support of the EPSRC grant EP/P000835/1. J.G. gratefully acknowledges support of the Baden-Württemberg fundation for the project “Numerical Methods for Multi-Phase Flows with Strongly Varying Mach Numbers”.

Keywords

A posteriori error analysis
Discontinuous Galerkin
Dual weighted residuals
Elastodynamics

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/978-3-319-57397-7_39

Cite this

Giesselmann, J., & Pryer, T. (2017). Goal-oriented error analysis of a DG scheme for a second gradient elastodynamics model. In C. Cances, & P. Omnes (Eds.), Finite Volumes for Complex Applications VIII—Methods and Theoretical Aspects - FVCA8 2017 (pp. 457-466). (Springer Proceedings in Mathematics and Statistics; Vol. 199). Springer New York. https://doi.org/10.1007/978-3-319-57397-7_39

Goal-oriented error analysis of a DG scheme for a second gradient elastodynamics model. / Giesselmann, Jan; Pryer, Tristan.
Finite Volumes for Complex Applications VIII—Methods and Theoretical Aspects - FVCA8 2017. ed. / Clement Cances; Pascal Omnes. Springer New York, 2017. p. 457-466 (Springer Proceedings in Mathematics and Statistics; Vol. 199).

Research output: Chapter or section in a book/report/conference proceeding › Chapter in a published conference proceeding

Giesselmann, J & Pryer, T 2017, Goal-oriented error analysis of a DG scheme for a second gradient elastodynamics model. in C Cances & P Omnes (eds), Finite Volumes for Complex Applications VIII—Methods and Theoretical Aspects - FVCA8 2017. Springer Proceedings in Mathematics and Statistics, vol. 199, Springer New York, pp. 457-466, 8th International Symposium on Finite Volumes for Complex Applications - Methods and Theoretical Aspects, FVCA8 2017, Lille, France, 12/06/17. https://doi.org/10.1007/978-3-319-57397-7_39

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Goal-oriented error analysis of a DG scheme for a second gradient elastodynamics model

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Keywords

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