Premium
Efficient space‐time adaptivity for parabolic evolution equations using wavelets in time and finite elements in space
Author(s) -
Venetië Raymond,
Westerdiep Jan
Publication year - 2023
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2457
Subject(s) - mathematics , tensor product , wavelet , bilinear interpolation , linear space , finite element method , space (punctuation) , parabolic partial differential equation , mathematical analysis , algorithm , pure mathematics , discrete mathematics , computer science , partial differential equation , statistics , physics , artificial intelligence , thermodynamics , operating system
Considering the space‐time adaptive method for parabolic evolution equations we introduced in Stevenson et al., this work discusses an implementation of the method in which every step is of linear complexity. Exploiting the tensor‐product structure of the space‐time cylinder, the method allows for a family of trial spaces given as spans of wavelets‐in‐time tensorized with 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.