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A wavelet-in-time, finite element-in-space adaptive method for parabolic evolution equations (2101.03956v3)
Published 11 Jan 2021 in math.NA and cs.NA
Abstract: 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.