Noether-Type Discrete Conserved Quantities Arising from a Finite Element Approximation of a Variational Problem

Elizabeth L. Mansfield, Tristan Pryer

Research output: Contribution to journalArticlepeer-review

1 Citation (SciVal)

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.

Original languageEnglish
Pages (from-to)729-762
Number of pages34
JournalFoundations of Computational Mathematics
Volume17
Issue number3
DOIs
Publication statusPublished - 1 Jun 2017

Keywords

  • Conserved quantities
  • Finite element method
  • Noether’s Theorem
  • Variational problem

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Noether-Type Discrete Conserved Quantities Arising from a Finite Element Approximation of a Variational Problem'. Together they form a unique fingerprint.

Cite this