Search

MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

MiS Preprint
33/2020

Existence of dynamical low-rank approximations to parabolic problems

Markus Bachmayr, Henrik Eisenmann, Emil Kieri and André Uschmajew

Abstract

The existence and uniqueness of weak solutions to dynamical low-rank evolution problems for parabolic partial differential equations in two spatial dimensions is shown, covering also non-diagonal diffusion in the elliptic part. The proof is based on a variational time-stepping scheme on the low-rank manifold. Moreover, this scheme is shown to be closely related to practical methods for computing such low-rank evolutions.

Received:
27.02.2020
Published:
27.02.2020

Related publications

inJournal
2021 Repository Open Access
Markus Bachmayr, Henrik Eisenmann, Emil Kieri and André Uschmajew

Existence of dynamical low-rank approximations to parabolic problems

In: Mathematics of computation, 90 (2021) 330, pp. 1799-1830