A wavelet-in-time, finite element-in-space adaptive method for parabolic evolution equations

In this work, an r -linearly converging adaptive solver is constructed for parabolic evolution equations in a simultaneous space-time variational formulation. Exploiting the product structure of the space-time cylinder, the family of trial spaces that we consider are given as the spans of wavelets-i...

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Bibliographic Details
Published in:Advances in computational mathematics 2022-06, Vol.48 (3), Article 17
Main Authors: Stevenson, Rob, van Venetië, Raymond, Westerdiep, Jan
Format: Article
Language:English
Subjects:
Computational mathematics
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Evolution
Finite element method
Mathematical analysis
Mathematical and Computational Biology
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Spacetime
Visualization
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Summary:In this work, an r -linearly converging adaptive solver is constructed for parabolic evolution equations in a simultaneous space-time variational formulation. Exploiting the product structure of the space-time cylinder, the family of trial spaces that we consider are given as the spans of wavelets-in-time and (locally refined) finite element spaces-in-space. Numerical results illustrate our theoretical findings.
ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-022-09930-w