Discrete Variational Derivative Methods for the EPDiff equation

2016/04/21 by Stig Larsson, Takayasu Matsuo, Larsson, Stig +5
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1604.06224

openalex publication_date 2016/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

Citations

• Interaction Dynamics of Singular Wave Fronts

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