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Discrete variational derivative methods: Geometric Integration methods for PDEs

Banff International Research Station for Mathematical Innovation and Discovery

Many PDEs arise from a variational principle, and this leads to many of their qualitative properties. The discrete variational method (DVDM) is a technique for discretising such a PDE directly from this variational principle. It derivation ensures that it reproduces dissipation/energy preserving properties of the underlying PDE. The performance of these method is often very good. In this talk I will show that this is because the discrete solution satisfies a modified equation, which in turn satisfies a (form of a) variational principle which is a perturbation of the original. Properties of the solution of the DVDM can then be derived directly from this modified variational equation. This is Joint work with akaharu Yaguchi (Kobe) and Daisuke Furihata (Osaka).

Mathematics; Numerical analysis

video/mp4

Author affiliation: University of Bath

2017-12-10

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63879

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/