Mansfield, Elizabeth L.,
Pryer, Tristan
(2014)
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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)
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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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