Advances in Computational Mathematics

, Volume 45, Issue 2, pp 1031–1066 | Cite as

An optimal adaptive tensor product wavelet solver of a space-time FOSLS formulation of parabolic evolution problems

  • Nikolaos Rekatsinas
  • Rob StevensonEmail author
Open Access


In this work, we construct a well-posed first-order system least squares (FOSLS) simultaneously space-time formulation of parabolic PDEs. Using an adaptive wavelet solver, this problem is solved with the best possible rate in linear complexity. Thanks to the use of a basis that consists of tensor products of wavelets in space and time, this rate is equal to that when solving the corresponding stationary problem. Our findings are illustrated by numerical results.


Parabolic PDEs Space-time variational formulation First order system least squares Adaptive wavelet solver Optimal rates Linear complexity 

Mathematics Subject Classification (2010)

35K20 41A25 41A63 42C40 65N12 65T60 65N30 


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Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Korteweg-de Vries Institute for MathematicsUniversity of AmsterdamAmsterdamThe Netherlands

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