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

01/11/2021

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by   Rob Stevenson, et al.

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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.