Two structure-preserving time discretizations for gradient flows
Numerical Analysis
2019-08-28 v2 Numerical Analysis
Abstract
The equality between dissipation and energy drop is a structural property of gradient-flow dynamics. The classical implicit Euler scheme fails to reproduce this equality at the discrete level. We discuss two modifications of the Euler scheme satisfying an exact energy equality at the discrete level. Existence of discrete solutions and their convergence as the fineness of the partition goes to zero are discussed. Eventually, we address extensions to generalized gradient flows, GENERIC flows, and curves of maximal slope in metric spaces.
Keywords
Cite
@article{arxiv.1811.06033,
title = {Two structure-preserving time discretizations for gradient flows},
author = {Ansgar Jüngel and Ulisse Stefanelli and Lara Trussardi},
journal= {arXiv preprint arXiv:1811.06033},
year = {2019}
}