Presented by:
Peter Hydon University of Kent
Date:
Wednesday 11th September 2019 - 14:00 to 15:00
Venue:
INI Seminar Room 2
Event:
Abstract:
A (local) conservation law of a given system of
differential or difference equations is a divergence expression that is zero on
all solutions. The Euler operator is a powerful tool in the formal theory of
conservation laws that enables key results to be proved simply, including
several generalizations of Noether's theorems.
This talk begins with a short survey of the main ideas and results.
The current method for inverting the divergence operator
generates many unnecessary terms by integrating in all directions
simultaneously. As a result, symbolic algebra packages create over-complicated
representations of conservation laws, making it difficult to obtain efficient
conservative finite difference approximations symbolically. A new approach
resolves this problem by using partial Euler operators to construct
near-optimal representations. The talk explains this approach, which was
developed during the GCS programme.
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