Can I read A Space-time Adaptive Low-rank Method for High-dimensional Parabolic Partial Differential Equations on EtoBox?

A Space-time Adaptive Low-rank Method for High-dimensional Parabolic Partial Differential Equations by Bachmayr, Markus; Faldum, Manfred is a scholarly article available to read on EtoBox.

What is A Space-time Adaptive Low-rank Method for High-dimensional Parabolic Partial Differential Equations about?

An adaptive method for parabolic partial differential equations that combines sparse wavelet expansions in time with adaptive low-rank approximations in the spatial variables is constructed and analyzed. The method is shown to converge and satisfy similar complexity bounds as existing adaptive low-rank methods for elliptic problems, establishing its suitability for parabolic problems on high-dimensional spatial domains. The construction also yields computable rigorous a posteriori error bounds for such problems. The results are illustrated by numerical experiments.

Author

Bachmayr, Markus; Faldum, Manfred

Published

2023

Language

EN