Higher order temporal finite element methods through mixed formalisms

The extended framework of Hamilton’s principle and the mixed convolved action principle provide new rigorous weak variational formalism for a broad range of initial boundary value problems in mathematical physics and mechanics. In this paper, their potential when adopting temporally higher order app...

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Autor principal: Kim, Jinkyu
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2014
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4159482/
https://www.ncbi.nlm.nih.gov/pubmed/25210664
http://dx.doi.org/10.1186/2193-1801-3-458
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author Kim, Jinkyu
author_facet Kim, Jinkyu
author_sort Kim, Jinkyu
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description The extended framework of Hamilton’s principle and the mixed convolved action principle provide new rigorous weak variational formalism for a broad range of initial boundary value problems in mathematical physics and mechanics. In this paper, their potential when adopting temporally higher order approximations is investigated. The classical single-degree-of-freedom dynamical systems are primarily considered to validate and to investigate the performance of the numerical algorithms developed from both formulations. For the undamped system, all the algorithms are symplectic and unconditionally stable with respect to the time step. For the damped system, they are shown to be accurate with good convergence characteristics.
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spelling pubmed-41594822014-09-10 Higher order temporal finite element methods through mixed formalisms Kim, Jinkyu Springerplus Research The extended framework of Hamilton’s principle and the mixed convolved action principle provide new rigorous weak variational formalism for a broad range of initial boundary value problems in mathematical physics and mechanics. In this paper, their potential when adopting temporally higher order approximations is investigated. The classical single-degree-of-freedom dynamical systems are primarily considered to validate and to investigate the performance of the numerical algorithms developed from both formulations. For the undamped system, all the algorithms are symplectic and unconditionally stable with respect to the time step. For the damped system, they are shown to be accurate with good convergence characteristics. Springer International Publishing 2014-08-23 /pmc/articles/PMC4159482/ /pubmed/25210664 http://dx.doi.org/10.1186/2193-1801-3-458 Text en © Kim; licensee Springer. 2014 This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.
spellingShingle Research
Kim, Jinkyu
Higher order temporal finite element methods through mixed formalisms
title Higher order temporal finite element methods through mixed formalisms
title_full Higher order temporal finite element methods through mixed formalisms
title_fullStr Higher order temporal finite element methods through mixed formalisms
title_full_unstemmed Higher order temporal finite element methods through mixed formalisms
title_short Higher order temporal finite element methods through mixed formalisms
title_sort higher order temporal finite element methods through mixed formalisms
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4159482/
https://www.ncbi.nlm.nih.gov/pubmed/25210664
http://dx.doi.org/10.1186/2193-1801-3-458
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