Efficient space-time adaptivity for parabolic evolution equations using wavelets in time and finite elements in space
Numerical Analysis
2021-04-20 v2 Numerical Analysis
Abstract
Considering the space-time adaptive method for parabolic evolution equations introduced in [arXiv:2101.03956 [math.NA]], this work discusses an implementation of the method in which every step is of linear complexity. Exploiting the product structure of the space-time cylinder, the method allows for a family of trial spaces given as the spans of wavelets-in-time tensorized with (locally refined) finite element spaces-in-space. On spaces whose bases are indexed by double-trees, we derive an algorithm that applies the resulting bilinear forms in linear complexity. We provide extensive numerical experiments to demonstrate the linear runtime of the resulting adaptive loop.
Cite
@article{arxiv.2104.08143,
title = {Efficient space-time adaptivity for parabolic evolution equations using wavelets in time and finite elements in space},
author = {Raymond van Venetië and Jan Westerdiep},
journal= {arXiv preprint arXiv:2104.08143},
year = {2021}
}