Existence of dynamical low-rank approximations to parabolic problems

02/27/2020

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by   Markus Bachmayr, et al.

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The existence of weak solutions of dynamical low-rank evolution 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.