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

被引：0
作者：
Rob Stevenson
Raymond van Venetië
Jan Westerdiep
机构：
[1] University of Amsterdam,Korteweg–de Vries (KdV) Institute for Mathematics
来源：
Advances in Computational Mathematics | 2022年 / 48卷
关键词：
Space-time variational formulations of parabolic PDEs; Quasi-best approximations; Least squares methods; Adaptive approximation; Tensor product approximation; Optimal preconditioners; 35K20; 65F08; 65M12; 65M60; 65T60;
D O I：
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学科分类号：
摘要：
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.
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