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.

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.

http://www.asc.tuwien.ac.at/preprint/2018/asc28x2018.pdf

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