Variation entropy

a continuous local generalization of the TVD property using entropy principles

Journal article (2019)

Authors

M.F.P. ten Eikelder Ship Hydromechanics and Structures - Mechanical, Maritime and Materials Engineering
I. Akkerman Ship Hydromechanics and Structures - Mechanical, Maritime and Materials Engineering
Research Group
Ship Hydromechanics and Structures (Mechanical, Maritime and Materials Engineering) (TU Delft)
Copyright: © 2019 M.F.P. ten Eikelder, I. Akkerman
DOI
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https://doi.org/10.1016/j.cma.2019.06.023
TVD property Variation entropy Entropy solutions Local continuous variation equations Nonlinear conservation laws
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Published Date

2019

Language

English

Faculty

Mechanical, Maritime and Materials Engineering

Department

Marine and Transport Technology

Research Group

Ship Hydromechanics and Structures

Abstract

This paper presents the notion of a variation entropy. This concept is an entropy framework for the gradient of the solution of a conservation law instead of on the solution itself. It appears that all semi-norms are admissible variation entropies. This provides insight into the total variation diminishing property and justifies it from entropy principles. The framework allows to derive new local variation diminishing properties in the continuous form. This can facilitate the design of new numerical methods for problems that contain discontinuities.