## 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 language | English |
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Pages (from-to) | 729-762 |

Number of pages | 34 |

Journal | Foundations of Computational Mathematics |

Volume | 17 |

Issue number | 3 |

DOIs | |

Publication status | Published - 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