Analytic regularity and solution approximation for a semilinear elliptic partial differential equation in a polygon

In an open, bounded Lipschitz polygon Ω ⊂ R 2 , we establish weighted analytic regularity for a semilinear, elliptic PDE with analytic nonlinearity and subject to a source term f which is analytic in Ω . The boundary conditions on each edge of ∂ Ω are either homogeneous Dirichlet or homogeneous Neum...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Calcolo 2024-03, Vol.61 (1), Article 11
Hauptverfasser:	He, Yanchen, Schwab, Christoph
Format:	Artikel
Sprache:	eng
Schlagworte:	Approximation Artificial neural networks Boundary conditions Dirichlet problem Finite element method Mathematics Mathematics and Statistics Numerical Analysis Partial differential equations Polygons Reduced order models Regularity Tensors Theory of Computation
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

container_end_page
container_issue	1
container_start_page
container_title	Calcolo
container_volume	61
creator	He, Yanchen Schwab, Christoph
description	In an open, bounded Lipschitz polygon Ω ⊂ R 2 , we establish weighted analytic regularity for a semilinear, elliptic PDE with analytic nonlinearity and subject to a source term f which is analytic in Ω . The boundary conditions on each edge of ∂ Ω are either homogeneous Dirichlet or homogeneous Neumann BCs. The presently established weighted analytic regularity of solutions implies exponential convergence of various approximation schemes: hp -finite elements, reduced order models via Kolmogorov n -widths of solution sets in H 1 ( Ω ) , quantized tensor formats and certain deep neural networks.
doi_str_mv	10.1007/s10092-023-00562-0
format	Article
fullrecord	<record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2913468521</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2913468521</sourcerecordid><originalsourceid>FETCH-LOGICAL-c363t-c5c303ad2c4153b8b2d0fdcc664409ca070a6bf0bb83be4459c5fb1b881a7ace3</originalsourceid><addsrcrecordid>eNp9kE1LxDAYhIMouK7-AU8Bz9U3H822x2XxCxa86DkkabJkybbdpAX7781uBW9e8mZgnoEZhO4JPBKA1VPKb00LoKwAKEX-XaAFIVQUJWf8Ei0AoCpAUH6NblLaZ1nyii9QWrcqTIM3ONrdGFT0w4RV2-DUhXHwXYtV38fu2x_UWbkuYoWTPfjgW6sitiH4_sT3Kg5eBdx452y07VnY4zhzPgfhvgvTrmtv0ZVTIdm737tEXy_Pn5u3Yvvx-r5ZbwvDBBsKUxoGTDXUcFIyXWnagGuMEYJzqI2CFSihHWhdMW05L2tTOk10VRG1UsayJXqYc3OB42jTIPfdGHPfJGlNGBdVSUl20dllYpdStE72MbeNkyQgT-PKeVyZx5XncSVkiM1QyuZ2Z-Nf9D_UD04cf8A</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2913468521</pqid></control><display><type>article</type><title>Analytic regularity and solution approximation for a semilinear elliptic partial differential equation in a polygon</title><source>SpringerLink Journals - AutoHoldings</source><creator>He, Yanchen ; Schwab, Christoph</creator><creatorcontrib>He, Yanchen ; Schwab, Christoph</creatorcontrib><description>In an open, bounded Lipschitz polygon Ω ⊂ R 2 , we establish weighted analytic regularity for a semilinear, elliptic PDE with analytic nonlinearity and subject to a source term f which is analytic in Ω . The boundary conditions on each edge of ∂ Ω are either homogeneous Dirichlet or homogeneous Neumann BCs. The presently established weighted analytic regularity of solutions implies exponential convergence of various approximation schemes: hp -finite elements, reduced order models via Kolmogorov n -widths of solution sets in H 1 ( Ω ) , quantized tensor formats and certain deep neural networks.</description><identifier>ISSN: 0008-0624</identifier><identifier>EISSN: 1126-5434</identifier><identifier>DOI: 10.1007/s10092-023-00562-0</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Approximation ; Artificial neural networks ; Boundary conditions ; Dirichlet problem ; Finite element method ; Mathematics ; Mathematics and Statistics ; Numerical Analysis ; Partial differential equations ; Polygons ; Reduced order models ; Regularity ; Tensors ; Theory of Computation</subject><ispartof>Calcolo, 2024-03, Vol.61 (1), Article 11</ispartof><rights>The Author(s) 2024</rights><rights>The Author(s) 2024. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c363t-c5c303ad2c4153b8b2d0fdcc664409ca070a6bf0bb83be4459c5fb1b881a7ace3</citedby><cites>FETCH-LOGICAL-c363t-c5c303ad2c4153b8b2d0fdcc664409ca070a6bf0bb83be4459c5fb1b881a7ace3</cites><orcidid>0000-0002-9722-0354</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10092-023-00562-0$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10092-023-00562-0$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,27923,27924,41487,42556,51318</link.rule.ids></links><search><creatorcontrib>He, Yanchen</creatorcontrib><creatorcontrib>Schwab, Christoph</creatorcontrib><title>Analytic regularity and solution approximation for a semilinear elliptic partial differential equation in a polygon</title><title>Calcolo</title><addtitle>Calcolo</addtitle><description>In an open, bounded Lipschitz polygon Ω ⊂ R 2 , we establish weighted analytic regularity for a semilinear, elliptic PDE with analytic nonlinearity and subject to a source term f which is analytic in Ω . The boundary conditions on each edge of ∂ Ω are either homogeneous Dirichlet or homogeneous Neumann BCs. The presently established weighted analytic regularity of solutions implies exponential convergence of various approximation schemes: hp -finite elements, reduced order models via Kolmogorov n -widths of solution sets in H 1 ( Ω ) , quantized tensor formats and certain deep neural networks.</description><subject>Approximation</subject><subject>Artificial neural networks</subject><subject>Boundary conditions</subject><subject>Dirichlet problem</subject><subject>Finite element method</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Numerical Analysis</subject><subject>Partial differential equations</subject><subject>Polygons</subject><subject>Reduced order models</subject><subject>Regularity</subject><subject>Tensors</subject><subject>Theory of Computation</subject><issn>0008-0624</issn><issn>1126-5434</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNp9kE1LxDAYhIMouK7-AU8Bz9U3H822x2XxCxa86DkkabJkybbdpAX7781uBW9e8mZgnoEZhO4JPBKA1VPKb00LoKwAKEX-XaAFIVQUJWf8Ei0AoCpAUH6NblLaZ1nyii9QWrcqTIM3ONrdGFT0w4RV2-DUhXHwXYtV38fu2x_UWbkuYoWTPfjgW6sitiH4_sT3Kg5eBdx452y07VnY4zhzPgfhvgvTrmtv0ZVTIdm737tEXy_Pn5u3Yvvx-r5ZbwvDBBsKUxoGTDXUcFIyXWnagGuMEYJzqI2CFSihHWhdMW05L2tTOk10VRG1UsayJXqYc3OB42jTIPfdGHPfJGlNGBdVSUl20dllYpdStE72MbeNkyQgT-PKeVyZx5XncSVkiM1QyuZ2Z-Nf9D_UD04cf8A</recordid><startdate>20240301</startdate><enddate>20240301</enddate><creator>He, Yanchen</creator><creator>Schwab, Christoph</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0002-9722-0354</orcidid></search><sort><creationdate>20240301</creationdate><title>Analytic regularity and solution approximation for a semilinear elliptic partial differential equation in a polygon</title><author>He, Yanchen ; Schwab, Christoph</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c363t-c5c303ad2c4153b8b2d0fdcc664409ca070a6bf0bb83be4459c5fb1b881a7ace3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Approximation</topic><topic>Artificial neural networks</topic><topic>Boundary conditions</topic><topic>Dirichlet problem</topic><topic>Finite element method</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Numerical Analysis</topic><topic>Partial differential equations</topic><topic>Polygons</topic><topic>Reduced order models</topic><topic>Regularity</topic><topic>Tensors</topic><topic>Theory of Computation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>He, Yanchen</creatorcontrib><creatorcontrib>Schwab, Christoph</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Calcolo</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>He, Yanchen</au><au>Schwab, Christoph</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Analytic regularity and solution approximation for a semilinear elliptic partial differential equation in a polygon</atitle><jtitle>Calcolo</jtitle><stitle>Calcolo</stitle><date>2024-03-01</date><risdate>2024</risdate><volume>61</volume><issue>1</issue><artnum>11</artnum><issn>0008-0624</issn><eissn>1126-5434</eissn><abstract>In an open, bounded Lipschitz polygon Ω ⊂ R 2 , we establish weighted analytic regularity for a semilinear, elliptic PDE with analytic nonlinearity and subject to a source term f which is analytic in Ω . The boundary conditions on each edge of ∂ Ω are either homogeneous Dirichlet or homogeneous Neumann BCs. The presently established weighted analytic regularity of solutions implies exponential convergence of various approximation schemes: hp -finite elements, reduced order models via Kolmogorov n -widths of solution sets in H 1 ( Ω ) , quantized tensor formats and certain deep neural networks.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s10092-023-00562-0</doi><orcidid>https://orcid.org/0000-0002-9722-0354</orcidid><oa>free_for_read</oa></addata></record>
fulltext	fulltext
identifier	ISSN: 0008-0624
ispartof	Calcolo, 2024-03, Vol.61 (1), Article 11
issn	0008-0624 1126-5434
language	eng
recordid	cdi_proquest_journals_2913468521
source	SpringerLink Journals - AutoHoldings
subjects	Approximation Artificial neural networks Boundary conditions Dirichlet problem Finite element method Mathematics Mathematics and Statistics Numerical Analysis Partial differential equations Polygons Reduced order models Regularity Tensors Theory of Computation
title	Analytic regularity and solution approximation for a semilinear elliptic partial differential equation in a polygon
url	https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-10T23%3A55%3A03IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Analytic%20regularity%20and%20solution%20approximation%20for%20a%20semilinear%20elliptic%20partial%20differential%20equation%20in%20a%20polygon&rft.jtitle=Calcolo&rft.au=He,%20Yanchen&rft.date=2024-03-01&rft.volume=61&rft.issue=1&rft.artnum=11&rft.issn=0008-0624&rft.eissn=1126-5434&rft_id=info:doi/10.1007/s10092-023-00562-0&rft_dat=%3Cproquest_cross%3E2913468521%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2913468521&rft_id=info:pmid/&rfr_iscdi=true