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Noether type discrete conserved quantities arising from a finite element approximation of a variational problem

Mansfield, Elizabeth L., Pryer, Tristan (2014) Noether type discrete conserved quantities arising from a finite element approximation of a variational problem. Foundations of Computational Mathematics, . pp. 1-34. ISSN 1615-3375. E-ISSN 1615-3383. (doi:10.1007/s10208-015-9298-0) (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)

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. (Contact us about this Publication)
Official URL
http://dx.doi.org/10.1007/s10208-015-9298-0

Abstract

In this work, we prove a weak Noether-type Theorem for a class of variational problems that admit broken extremals. We use this result to prove discrete Noether-type conservation laws for a conforming finite element discretisation of a model elliptic problem. In addition, we study how well the finite element scheme satisfies the continuous conservation laws arising from the application of Noether’s first theorem (1918). We summarise extensive numerical tests, illustrating the conservation of the discrete Noether law using the p-Laplacian as an example and derive a geometric-based adaptive algorithm where an appropriate Noether quantity is the goal functional.

Item Type: Article
DOI/Identification number: 10.1007/s10208-015-9298-0
Projects: [UNSPECIFIED] Group actions in function approximation spaces
Uncontrolled keywords: Finite element method; Conserved quantities; Noether’s Theorem; Variational problem
Subjects: Q Science > QA Mathematics (inc Computing science) > QA297 Numerical analysis
Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations
Q Science > QA Mathematics (inc Computing science) > QA387 Basic Lie theory
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Elizabeth L Mansfield
Date Deposited: 10 Jun 2015 09:47 UTC
Last Modified: 29 May 2019 14:42 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/48995 (The current URI for this page, for reference purposes)
Mansfield, Elizabeth L.: https://orcid.org/0000-0002-6778-2241
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