An optimal adaptive wavelet method for first order system least squares

In this paper, it is shown that any well-posed 2nd order PDE can be reformulated as a well-posed first order least squares system. This system will be solved by an adaptive wavelet solver in optimal computational complexity. The applications that are considered are second order elliptic PDEs with ge...

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Detalles Bibliográficos
Autores principales: Rekatsinas, Nikolaos, Stevenson, Rob
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2018
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6061829/
https://www.ncbi.nlm.nih.gov/pubmed/30100635
http://dx.doi.org/10.1007/s00211-018-0961-7
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author Rekatsinas, Nikolaos
Stevenson, Rob
author_facet Rekatsinas, Nikolaos
Stevenson, Rob
author_sort Rekatsinas, Nikolaos
collection PubMed
description In this paper, it is shown that any well-posed 2nd order PDE can be reformulated as a well-posed first order least squares system. This system will be solved by an adaptive wavelet solver in optimal computational complexity. The applications that are considered are second order elliptic PDEs with general inhomogeneous boundary conditions, and the stationary Navier–Stokes equations.
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spelling pubmed-60618292018-08-09 An optimal adaptive wavelet method for first order system least squares Rekatsinas, Nikolaos Stevenson, Rob Numer Math (Heidelb) Article In this paper, it is shown that any well-posed 2nd order PDE can be reformulated as a well-posed first order least squares system. This system will be solved by an adaptive wavelet solver in optimal computational complexity. The applications that are considered are second order elliptic PDEs with general inhomogeneous boundary conditions, and the stationary Navier–Stokes equations. Springer Berlin Heidelberg 2018-03-24 2018 /pmc/articles/PMC6061829/ /pubmed/30100635 http://dx.doi.org/10.1007/s00211-018-0961-7 Text en © The Author(s) 2018 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), 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.
spellingShingle Article
Rekatsinas, Nikolaos
Stevenson, Rob
An optimal adaptive wavelet method for first order system least squares
title An optimal adaptive wavelet method for first order system least squares
title_full An optimal adaptive wavelet method for first order system least squares
title_fullStr An optimal adaptive wavelet method for first order system least squares
title_full_unstemmed An optimal adaptive wavelet method for first order system least squares
title_short An optimal adaptive wavelet method for first order system least squares
title_sort optimal adaptive wavelet method for first order system least squares
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6061829/
https://www.ncbi.nlm.nih.gov/pubmed/30100635
http://dx.doi.org/10.1007/s00211-018-0961-7
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