Existence of dynamical low-rank approximations to parabolic problems

2020/02/27 by Bachmayr, Markus, Eisenmann, Henrik, Kieri, Emil +1 · 2 citations
#35K15 #35R01 (Primary) 15A69 #65L05 (Secondary) #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2002.12197

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.

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