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.
|Journal||Computer Methods in Applied Mechanics and Engineering|
|Publication status||Published - 2019|
- Entropy solutions
- Local continuous variation equations
- Nonlinear conservation laws
- TVD property
- Variation entropy