DG and hp-DG for highly indefinite Helmholtz problems

DG and hp-DG for highly indefinite Helmholtz problems

We develop a stability and convergence theory for a Discontinuous Galerkin formulation (DG) of a highly indefinite Helmholtz problem in ${\rm I\!R}^d, d \in \{2,3\}$. We prove that the DG‐method admits a unique solution under much weaker conditions than for conventional Galerkin methods. It is shown...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Proceedings in applied mathematics and mechanics 2013-12, Vol.13 (1), p.443-444
Hauptverfasser: Melenk, Jens Markus, Parsania, Asieh, Sauter, Stefan
Format: Artikel
Sprache:eng
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 444
container_issue 1
container_start_page 443
container_title Proceedings in applied mathematics and mechanics
container_volume 13
creator Melenk, Jens Markus
Parsania, Asieh
Sauter, Stefan
description We develop a stability and convergence theory for a Discontinuous Galerkin formulation (DG) of a highly indefinite Helmholtz problem in ${\rm I\!R}^d, d \in \{2,3\}$. We prove that the DG‐method admits a unique solution under much weaker conditions than for conventional Galerkin methods. It is shown that for the case of hp‐DGFEM the optimal convergence order estimate can be obtained under the conditions that $kh/\sqrt{p}$ is sufficiently small and the polynomial degree p is at least O(log k). (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
doi_str_mv 10.1002/pamm.201310215
format Article
fullrecord <record><control><sourceid>wiley_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1002_pamm_201310215</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>PAMM201310215</sourcerecordid><originalsourceid>FETCH-LOGICAL-c1275-6d600be11953ae8c92bf2e1fc88a8c1237c44d11f81200a26641f0b867a4fc453</originalsourceid><addsrcrecordid>eNqFj8FLwzAUh4MoOKdXz_0HOt9L2qQ9jqmbbFPBieAlpG1io-1aksKcf70dk7Gbp_c7fN-Dj5BrhBEC0JtW1fWIAjIEivEJGSBHEQrgeHq0z8mF9589j5zBgMS300Cti6Bsw36ZxgWl_SirbWDXhTZ2bTsdzHRVl03V_QSta7JK1_6SnBlVeX31d4fk9f5uNZmFi6fpw2S8CHOkIg55wQEyjZjGTOkkT2lmqEaTJ4lKeoSJPIoKRJMgBVCU8wgNZAkXKjJ5FLMhGe3_5q7x3mkjW2dr5bYSQe6i5S5aHqJ7Id0LG1vp7T-0fB4vl8duuHet7_T3wVXuS3LBRCzfHqcyfcH3FUZzOWe_He1o1g</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>DG and hp-DG for highly indefinite Helmholtz problems</title><source>Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals</source><source>Wiley Online Library All Journals</source><creator>Melenk, Jens Markus ; Parsania, Asieh ; Sauter, Stefan</creator><creatorcontrib>Melenk, Jens Markus ; Parsania, Asieh ; Sauter, Stefan</creatorcontrib><description>We develop a stability and convergence theory for a Discontinuous Galerkin formulation (DG) of a highly indefinite Helmholtz problem in ${\rm I\!R}^d, d \in \{2,3\}$. We prove that the DG‐method admits a unique solution under much weaker conditions than for conventional Galerkin methods. It is shown that for the case of hp‐DGFEM the optimal convergence order estimate can be obtained under the conditions that $kh/\sqrt{p}$ is sufficiently small and the polynomial degree p is at least O(log k). (© 2013 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)</description><identifier>ISSN: 1617-7061</identifier><identifier>EISSN: 1617-7061</identifier><identifier>DOI: 10.1002/pamm.201310215</identifier><language>eng</language><publisher>Berlin: WILEY-VCH Verlag</publisher><ispartof>Proceedings in applied mathematics and mechanics, 2013-12, Vol.13 (1), p.443-444</ispartof><rights>Copyright © 2013 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim</rights><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c1275-6d600be11953ae8c92bf2e1fc88a8c1237c44d11f81200a26641f0b867a4fc453</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fpamm.201310215$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fpamm.201310215$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,780,784,1417,27924,27925,45574,45575</link.rule.ids></links><search><creatorcontrib>Melenk, Jens Markus</creatorcontrib><creatorcontrib>Parsania, Asieh</creatorcontrib><creatorcontrib>Sauter, Stefan</creatorcontrib><title>DG and hp-DG for highly indefinite Helmholtz problems</title><title>Proceedings in applied mathematics and mechanics</title><addtitle>Proc. Appl. Math. Mech</addtitle><description>We develop a stability and convergence theory for a Discontinuous Galerkin formulation (DG) of a highly indefinite Helmholtz problem in ${\rm I\!R}^d, d \in \{2,3\}$. We prove that the DG‐method admits a unique solution under much weaker conditions than for conventional Galerkin methods. It is shown that for the case of hp‐DGFEM the optimal convergence order estimate can be obtained under the conditions that $kh/\sqrt{p}$ is sufficiently small and the polynomial degree p is at least O(log k). (© 2013 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)</description><issn>1617-7061</issn><issn>1617-7061</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><recordid>eNqFj8FLwzAUh4MoOKdXz_0HOt9L2qQ9jqmbbFPBieAlpG1io-1aksKcf70dk7Gbp_c7fN-Dj5BrhBEC0JtW1fWIAjIEivEJGSBHEQrgeHq0z8mF9589j5zBgMS300Cti6Bsw36ZxgWl_SirbWDXhTZ2bTsdzHRVl03V_QSta7JK1_6SnBlVeX31d4fk9f5uNZmFi6fpw2S8CHOkIg55wQEyjZjGTOkkT2lmqEaTJ4lKeoSJPIoKRJMgBVCU8wgNZAkXKjJ5FLMhGe3_5q7x3mkjW2dr5bYSQe6i5S5aHqJ7Id0LG1vp7T-0fB4vl8duuHet7_T3wVXuS3LBRCzfHqcyfcH3FUZzOWe_He1o1g</recordid><startdate>201312</startdate><enddate>201312</enddate><creator>Melenk, Jens Markus</creator><creator>Parsania, Asieh</creator><creator>Sauter, Stefan</creator><general>WILEY-VCH Verlag</general><general>WILEY‐VCH Verlag</general><scope>BSCLL</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>201312</creationdate><title>DG and hp-DG for highly indefinite Helmholtz problems</title><author>Melenk, Jens Markus ; Parsania, Asieh ; Sauter, Stefan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c1275-6d600be11953ae8c92bf2e1fc88a8c1237c44d11f81200a26641f0b867a4fc453</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><toplevel>online_resources</toplevel><creatorcontrib>Melenk, Jens Markus</creatorcontrib><creatorcontrib>Parsania, Asieh</creatorcontrib><creatorcontrib>Sauter, Stefan</creatorcontrib><collection>Istex</collection><collection>CrossRef</collection><jtitle>Proceedings in applied mathematics and mechanics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Melenk, Jens Markus</au><au>Parsania, Asieh</au><au>Sauter, Stefan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>DG and hp-DG for highly indefinite Helmholtz problems</atitle><jtitle>Proceedings in applied mathematics and mechanics</jtitle><addtitle>Proc. Appl. Math. Mech</addtitle><date>2013-12</date><risdate>2013</risdate><volume>13</volume><issue>1</issue><spage>443</spage><epage>444</epage><pages>443-444</pages><issn>1617-7061</issn><eissn>1617-7061</eissn><abstract>We develop a stability and convergence theory for a Discontinuous Galerkin formulation (DG) of a highly indefinite Helmholtz problem in ${\rm I\!R}^d, d \in \{2,3\}$. We prove that the DG‐method admits a unique solution under much weaker conditions than for conventional Galerkin methods. It is shown that for the case of hp‐DGFEM the optimal convergence order estimate can be obtained under the conditions that $kh/\sqrt{p}$ is sufficiently small and the polynomial degree p is at least O(log k). (© 2013 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)</abstract><cop>Berlin</cop><pub>WILEY-VCH Verlag</pub><doi>10.1002/pamm.201310215</doi><tpages>2</tpages></addata></record>
fulltext fulltext
identifier ISSN: 1617-7061
ispartof Proceedings in applied mathematics and mechanics, 2013-12, Vol.13 (1), p.443-444
issn 1617-7061
1617-7061
language eng
recordid cdi_crossref_primary_10_1002_pamm_201310215
source Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Wiley Online Library All Journals
title DG and hp-DG for highly indefinite Helmholtz problems
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-05T20%3A31%3A39IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-wiley_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=DG%20and%20hp-DG%20for%20highly%20indefinite%20Helmholtz%20problems&rft.jtitle=Proceedings%20in%20applied%20mathematics%20and%20mechanics&rft.au=Melenk,%20Jens%20Markus&rft.date=2013-12&rft.volume=13&rft.issue=1&rft.spage=443&rft.epage=444&rft.pages=443-444&rft.issn=1617-7061&rft.eissn=1617-7061&rft_id=info:doi/10.1002/pamm.201310215&rft_dat=%3Cwiley_cross%3EPAMM201310215%3C/wiley_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true