607 RWTH Publication No: 951716        2023       
TITLE A space-time adaptive low-rank method for high-dimensional parabolic partial differential equations
AUTHORS Markus Bachmayr, Manfred Faldum
ABSTRACT 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.
KEYWORDS Parabolic partial differential equationsHigh dimensionsSpace-time adaptive methodsLow-rank tensor approximationsWavelet approximationOperator compression
DOI 10.1016/j.jco.2024.101839
PUBLICATION Journal of complexity
Volume 82, June 2024, No. 101839