Contributions to Books:
A. Jüngel, U. Stefanelli, L. Trussardi:
"Two time discretizations for gradient flows exactly replicating energy dissipation";
in: "ASC Report 28/2018",
issued by: Institute for Analysis and Scientific Computing;
Vienna University of Technology,
Wien,
2018,
ISBN: 978-3-902627-11-7,
1
- 26.
English abstract:
The classical implicit Euler scheme fails to reproduce the exact dissipation dynamics of gradient flows: The discrete dissipation necessarily does not correspond to the energy drop. 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.
Electronic version of the publication:
http://www.asc.tuwien.ac.at/preprint/2018/asc28x2018.pdf
Created from the Publication Database of the Vienna University of Technology.