Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations

In a recent work (Feischl et al. in Eng Anal Bound Elem 62:141–153, 2016), we analyzed a weighted-residual error estimator for isogeometric boundary element methods in 2D and proposed an adaptive algorithm which steers the local mesh-refinement of the underlying partition as well as the multiplicity...

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Autores principales: Feischl, Michael, Gantner, Gregor, Haberl, Alexander, Praetorius, Dirk
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2016
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5445587/
https://www.ncbi.nlm.nih.gov/pubmed/28615749
http://dx.doi.org/10.1007/s00211-016-0836-8
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author Feischl, Michael
Gantner, Gregor
Haberl, Alexander
Praetorius, Dirk
author_facet Feischl, Michael
Gantner, Gregor
Haberl, Alexander
Praetorius, Dirk
author_sort Feischl, Michael
collection PubMed
description In a recent work (Feischl et al. in Eng Anal Bound Elem 62:141–153, 2016), we analyzed a weighted-residual error estimator for isogeometric boundary element methods in 2D and proposed an adaptive algorithm which steers the local mesh-refinement of the underlying partition as well as the multiplicity of the knots. In the present work, we give a mathematical proof that this algorithm leads to convergence even with optimal algebraic rates. Technical contributions include a novel mesh-size function which also monitors the knot multiplicity as well as inverse estimates for NURBS in fractional-order Sobolev norms.
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spelling pubmed-54455872017-06-12 Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations Feischl, Michael Gantner, Gregor Haberl, Alexander Praetorius, Dirk Numer Math (Heidelb) Article In a recent work (Feischl et al. in Eng Anal Bound Elem 62:141–153, 2016), we analyzed a weighted-residual error estimator for isogeometric boundary element methods in 2D and proposed an adaptive algorithm which steers the local mesh-refinement of the underlying partition as well as the multiplicity of the knots. In the present work, we give a mathematical proof that this algorithm leads to convergence even with optimal algebraic rates. Technical contributions include a novel mesh-size function which also monitors the knot multiplicity as well as inverse estimates for NURBS in fractional-order Sobolev norms. Springer Berlin Heidelberg 2016-08-11 2017 /pmc/articles/PMC5445587/ /pubmed/28615749 http://dx.doi.org/10.1007/s00211-016-0836-8 Text en © The Author(s) 2016 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
Feischl, Michael
Gantner, Gregor
Haberl, Alexander
Praetorius, Dirk
Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations
title Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations
title_full Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations
title_fullStr Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations
title_full_unstemmed Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations
title_short Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations
title_sort optimal convergence for adaptive iga boundary element methods for weakly-singular integral equations
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5445587/
https://www.ncbi.nlm.nih.gov/pubmed/28615749
http://dx.doi.org/10.1007/s00211-016-0836-8
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AT haberlalexander optimalconvergenceforadaptiveigaboundaryelementmethodsforweaklysingularintegralequations
AT praetoriusdirk optimalconvergenceforadaptiveigaboundaryelementmethodsforweaklysingularintegralequations

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