Discrete Variational Derivative Methods for the EPDiff equation
Analysis of PDEs
2016-04-26 v1 Numerical Analysis
Abstract
The aim of this paper is the derivation of structure preserving schemes for the solution of the EPDiff equation, with particular emphasis on the two dimensional case. We develop three different schemes based on the Discrete Variational Derivative Method (DVDM) on a rectangular domain discretized with a regular, structured, orthogonal grid. We present numerical experiments to support our claims: we investigate the preservation of energy and linear momenta, the reversibility, and the empirical convergence of the schemes. The quality of our schemes is finally tested by simulating the interaction of singular wave fronts.
Keywords
Cite
@article{arxiv.1604.06224,
title = {Discrete Variational Derivative Methods for the EPDiff equation},
author = {Stig Larsson and Takayasu Matsuo and Klas Modin and Matteo Molteni},
journal= {arXiv preprint arXiv:1604.06224},
year = {2016}
}
Comments
41 pages, 41 figures