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

Mansfield, E. L. and Pryer, T. (2017) Noether-type discrete conserved quantities arising from a finite element approximation of a variational problem. Foundations of Computational Mathematics, 17 (3). pp. 729-762. ISSN 1615-3375

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To link to this item DOI: 10.1007/s10208-015-9298-0

Abstract/Summary

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
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:51886
Publisher:Springer

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