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Towards a variational complex for the finite element method

Mansfield, Elizabeth L., Quispel, R. (2005) Towards a variational complex for the finite element method. Group Theory and Numerical Analysis, 39 . pp. 207-232. (doi:10.1090/crmp/039/15) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:714)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided.
Official URL:
https://doi.org/10.1090/crmp/039/15

Abstract

Variational and symplectic integrators are now popular for mechanical systems, both because of their good long term stability and qualitative fit. Sucy integrators mimic or inherit the Lagrangian, respectively Hamiltonian, structure of the continuous model. A variational complex is a theoretical tool for the rigorous study of Lagrangian systems and their conservation laws. This article examines whether a formulation of a variational calculus for finite element methods, for an arbitrary finite element approximation scheme, is possible. The motivation is that this would allow a variational scheme to be written down for a given approximation model. Moreover, the stability and the conservation laws of such integrators could be studied without any need for individual, ad hoc arguments. A number of examples are considered, mainly one-dimensional, and conditions for a suitable complex derived.

Item Type: Article
DOI/Identification number: 10.1090/crmp/039/15
Uncontrolled keywords: Ordinary differential-equations; conservation-laws; inverse problem; moving coframes; lie symmetries; calculus; foundations
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Elizabeth Mansfield
Date Deposited: 19 Dec 2007 18:26 UTC
Last Modified: 09 Mar 2023 11:29 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/714 (The current URI for this page, for reference purposes)

University of Kent Author Information

Mansfield, Elizabeth L..

Creator's ORCID: https://orcid.org/0000-0002-6778-2241
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