Takaharu Yaguchi - The Discrete Variational Derivative Method Based on Discrete Differential Forms

This week's "Seminar in analysis" is a joint seminar with Geometric integration.
Our guest Takaharu Yaguchi is talking about designing energy preserving schemes for PDEs, based on discrete variational derivatives / differential forms.

Speaker: Takaharu Yaguchi (The University of Tokyo)

Title: The Discrete Variational Derivative Method Based on Discrete Differential Forms

Abstract: As is well known, for PDEs that enjoy a conservation or dissipation property, numerical schemes that inherit the property are often advantageous in that the schemes are fairly stable and give qualitatively better numerical solutions in practice.

Lately, Furihata and Matsuo have developed the so-called “discrete variational derivative method” that automatically constructs energy preserving or dissipative finite difference schemes. Although this method was originally developed on uniform meshes, the use of non-uniform meshes is of importance for multi-dimensional problems.

In this talk, we will show an extension of this method to triangular meshes. This extension is achieved by combination of this method and the theory of the discrete differential forms by Bochev and Hyman.