Existence of dynamical low-rank approximations to parabolic problems
Numerical Analysis
2020-12-08 v3 Numerical Analysis
Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.2002.12197,
title = {Existence of dynamical low-rank approximations to parabolic problems},
author = {Markus Bachmayr and Henrik Eisenmann and Emil Kieri and André Uschmajew},
journal= {arXiv preprint arXiv:2002.12197},
year = {2020}
}