Variation entropy: a continuous local generalization of the TVD property using entropy principles

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3 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)261-283
JournalComputer Methods in Applied Mechanics and Engineering
Volume355
DOIs
Publication statusPublished - 2019

Keywords

  • Entropy solutions
  • Local continuous variation equations
  • Nonlinear conservation laws
  • TVD property
  • Variation entropy

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