{"id":"https://openalex.org/W2029966922","doi":"https://doi.org/10.1090/s0025-5718-10-02362-8","title":"Convergence analysis for finite element discretizations of the Helmholtz equation with Dirichlet-to-Neumann boundary conditions","display_name":"Convergence analysis for finite element discretizations of the Helmholtz equation with Dirichlet-to-Neumann boundary conditions","publication_year":2010,"publication_date":"2010-04-27","ids":{"openalex":"https://openalex.org/W2029966922","doi":"https://doi.org/10.1090/s0025-5718-10-02362-8","mag":"2029966922"},"language":"lv","primary_location":{"id":"doi:10.1090/s0025-5718-10-02362-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-10-02362-8","pdf_url":"https://www.ams.org/mcom/2010-79-272/S0025-5718-10-02362-8/S0025-5718-10-02362-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2010-79-272/S0025-5718-10-02362-8/S0025-5718-10-02362-8.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058356670","display_name":"Jens Markus Melenk","orcid":"https://orcid.org/0000-0001-9024-6028"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"J. Melenk","raw_affiliation_strings":["Institut f\u00c3\u00bcr Analysis und Scientific Computing, Technische Universit\u00c3\u00a4t Wien, Wiedner Hauptstrasse 8-10, A-1040 Wien, Austria","Institut f\u00fcr Analysis und Scientific Computing, Technische Universit\u00e4t Wien, Wiedner Hauptstrasse 8-10, A-1040 Wien, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00c3\u00bcr Analysis und Scientific Computing, Technische Universit\u00c3\u00a4t Wien, Wiedner Hauptstrasse 8-10, A-1040 Wien, Austria","institution_ids":["https://openalex.org/I145847075"]},{"raw_affiliation_string":"Institut f\u00fcr Analysis und Scientific Computing, Technische Universit\u00e4t Wien, Wiedner Hauptstrasse 8-10, A-1040 Wien, Austria","institution_ids":["https://openalex.org/I145847075"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049235940","display_name":"Stefan Sauter","orcid":"https://orcid.org/0000-0002-1403-1874"},"institutions":[{"id":"https://openalex.org/I202697423","display_name":"University of Zurich","ror":"https://ror.org/02crff812","country_code":"CH","type":"education","lineage":["https://openalex.org/I202697423"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"S. Sauter","raw_affiliation_strings":["Institut f\u00c3\u00bcr Mathematik, Universit\u00c3\u00a4t Z\u00c3\u00bcrich, Winterthurerstr 190, CH-8057 Z\u00c3\u00bcrich, Switzerland","Institut f\u00fcr Mathematik, Universit\u00e4t Z\u00fcrich, Winterthurerstr. 190, CH-8057, Z\u00fcrich, Switzerland#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00c3\u00bcr Mathematik, Universit\u00c3\u00a4t Z\u00c3\u00bcrich, Winterthurerstr 190, CH-8057 Z\u00c3\u00bcrich, Switzerland","institution_ids":["https://openalex.org/I202697423"]},{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Universit\u00e4t Z\u00fcrich, Winterthurerstr. 190, CH-8057, Z\u00fcrich, Switzerland#TAB#","institution_ids":["https://openalex.org/I202697423"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":12.3966,"has_fulltext":true,"cited_by_count":209,"citation_normalized_percentile":{"value":0.99121644,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"79","issue":"272","first_page":"1871","last_page":"1914"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.685017466545105},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42479807138442993},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4066631495952606},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3857060968875885}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.685017466545105},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42479807138442993},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4066631495952606},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3857060968875885}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1090/s0025-5718-10-02362-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-10-02362-8","pdf_url":"https://www.ams.org/mcom/2010-79-272/S0025-5718-10-02362-8/S0025-5718-10-02362-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:doi:10.5167/uzh-47459","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.190.179","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.190.179","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/journals/mcom/0000-000-00/S0025-5718-10-02362-8/S0025-5718-10-02362-8.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.568.6735","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.568.6735","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://mathweb.unizh.ch/fileadmin/math/preprints/09_08.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.958.9887","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.958.9887","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://anum.tuwien.ac.at/%7Emelenk/publications/melenk_sauter_I.pdf","raw_type":"text"},{"id":"doi:10.5167/uzh-47459","is_oa":true,"landing_page_url":"https://doi.org/10.5167/uzh-47459","pdf_url":null,"source":{"id":"https://openalex.org/S7407051291","display_name":"Universit\u00e4t Z\u00fcrich, ZORA","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-10-02362-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-10-02362-8","pdf_url":"https://www.ams.org/mcom/2010-79-272/S0025-5718-10-02362-8/S0025-5718-10-02362-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":52,"referenced_works":["https://openalex.org/W59705922","https://openalex.org/W137638080","https://openalex.org/W151351324","https://openalex.org/W177735991","https://openalex.org/W571822206","https://openalex.org/W604181985","https://openalex.org/W1488877410","https://openalex.org/W1492326914","https://openalex.org/W1504642953","https://openalex.org/W1533889494","https://openalex.org/W1602383637","https://openalex.org/W1967469744","https://openalex.org/W1969923739","https://openalex.org/W1972485395","https://openalex.org/W1978548050","https://openalex.org/W1995613081","https://openalex.org/W1998739679","https://openalex.org/W2000981618","https://openalex.org/W2001019613","https://openalex.org/W2006143998","https://openalex.org/W2008747183","https://openalex.org/W2019072617","https://openalex.org/W2021567871","https://openalex.org/W2021615646","https://openalex.org/W2025124289","https://openalex.org/W2030028670","https://openalex.org/W2037092148","https://openalex.org/W2041523977","https://openalex.org/W2045704682","https://openalex.org/W2053149981","https://openalex.org/W2056040698","https://openalex.org/W2057817591","https://openalex.org/W2061455778","https://openalex.org/W2068768492","https://openalex.org/W2071928229","https://openalex.org/W2081338783","https://openalex.org/W2082485912","https://openalex.org/W2084384915","https://openalex.org/W2091078702","https://openalex.org/W2115850109","https://openalex.org/W2120062331","https://openalex.org/W2139794367","https://openalex.org/W2150892223","https://openalex.org/W2157005274","https://openalex.org/W2168644075","https://openalex.org/W2170228337","https://openalex.org/W4210885577","https://openalex.org/W4232597038","https://openalex.org/W4243952940","https://openalex.org/W4252065595","https://openalex.org/W4290828441","https://openalex.org/W4292166829"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2042127053","https://openalex.org/W2142036596"],"abstract_inverted_index":{"A":[0],"rigorous":[1],"convergence":[2],"theory":[3],"for":[4,7,158],"Galerkin":[5],"methods":[6],"a":[8,109],"model":[9,160],"Helmholtz":[10],"problem":[11,161],"in":[12],"<inline-formula":[13,44,116,139,169,185,202,230,260,275],"content-type=\"math/mathml\">":[14,45,117,140,170,186,203,231,261,276],"<mml:math":[15,46,118,141,171,187,204,232,262,277],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[16,47,119,142,172,188,205,233,263,278],"alttext=\"double-struck":[17],"upper":[18],"R":[19],"Superscript":[20],"d\">":[21],"<mml:semantics>":[22,57,122,145,174,190,207,238,265,285],"<mml:msup>":[23],"<mml:mrow":[24,26,32,242],"class=\"MJX-TeXAtom-ORD\">":[25,27,33,243],"<mml:mi":[28],"mathvariant=\"double-struck\">R</mml:mi>":[29],"</mml:mrow>":[30,31,35,74,126,149,245,247,297],"<mml:mi>d</mml:mi>":[34,59],"</mml:msup>":[36],"<mml:annotation":[37,75,127,150,176,192,209,248,267,298],"encoding=\"application/x-tex\">{\\mathbb":[38],"{R}}^{d}</mml:annotation>":[39],"</mml:semantics>":[40,79,129,152,178,194,211,250,269,301],"</mml:math>":[41,80,130,153,179,195,212,251,270,302],"</inline-formula>":[42,81,131,154,180,196,213,252,271,303],",":[43,181,197],"alttext=\"d":[48],"element-of":[49],"StartSet":[50],"1":[51],"comma":[52,54],"2":[53],"3":[55],"EndSet\">":[56],"<mml:mrow>":[58,123,146,239,286],"<mml:mo>":[60,291],"\u2208":[61],"</mml:mo>":[62,293],"<mml:mo":[63,71,288,295],"fence=\"false\"":[64,72],"stretchy=\"false\">{</mml:mo>":[65],"<mml:mn>1</mml:mn>":[66],"<mml:mo>,</mml:mo>":[67,69],"<mml:mn>2</mml:mn>":[68],"<mml:mn>3</mml:mn>":[70],"stretchy=\"false\">}</mml:mo>":[73],"encoding=\"application/x-tex\">d":[76],"\\in":[77],"\\{1,2,3\\}</mml:annotation>":[78],"is":[82,156,214,220,224,253,272],"presented.":[83],"General":[84],"conditions":[85,228],"on":[86,165],"the":[87,91,100,106,114,134,159,163,166,182,199,227,257],"approximation":[88,92,183],"properties":[89],"of":[90,99,105,113,133],"space":[93],"are":[94],"stated":[95],"that":[96,222,229],"ensure":[97],"quasi-optimality":[98,223],"method.":[101],"As":[102],"an":[103],"application":[104],"general":[107],"theory,":[108],"full":[110],"error":[111],"analysis":[112],"classical":[115],"alttext=\"h":[120,143],"p\">":[121,144,237],"<mml:mi>h</mml:mi>":[124,147,175,241],"<mml:mi>p</mml:mi>":[125,148,191,246,266],"encoding=\"application/x-tex\">hp</mml:annotation>":[128,151],"-version":[132],"finite":[135],"element":[136],"method":[137],"(":[138],"-FEM)":[155],"presented":[157],"where":[162],"dependence":[164],"mesh":[167],"width":[168],"alttext=\"h\">":[173],"encoding=\"application/x-tex\">h</mml:annotation>":[177],"order":[184],"alttext=\"p\">":[189,264],"encoding=\"application/x-tex\">p</mml:annotation>":[193,268],"and":[198,256],"wave":[200],"number":[201],"alttext=\"k\">":[206],"<mml:mi>k</mml:mi>":[208,240,294],"encoding=\"application/x-tex\">k</mml:annotation>":[210],"given":[215],"explicitly.":[216],"In":[217],"particular,":[218],"it":[219],"shown":[221],"obtained":[225],"under":[226],"alttext=\"k":[234],"h":[235],"slash":[236],"<mml:mo>/</mml:mo>":[244],"encoding=\"application/x-tex\">kh/p</mml:annotation>":[249],"sufficiently":[254],"small":[255],"polynomial":[258],"degree":[259],"at":[273],"least":[274],"alttext=\"upper":[279],"O":[280],"left-parenthesis":[281],"log":[282],"k":[283],"right-parenthesis\">":[284],"<mml:mi>O</mml:mi>":[287],"stretchy=\"false\">(</mml:mo>":[289],"<mml:mi>log</mml:mi>":[290],"\u2061":[292],"stretchy=\"false\">)</mml:mo>":[296],"encoding=\"application/x-tex\">O(\\log":[299],"k)</mml:annotation>":[300],".":[304]},"counts_by_year":[{"year":2026,"cited_by_count":11},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":23},{"year":2023,"cited_by_count":17},{"year":2022,"cited_by_count":14},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":21},{"year":2019,"cited_by_count":22},{"year":2018,"cited_by_count":11},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":12},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":12},{"year":2012,"cited_by_count":14}],"updated_date":"2026-06-19T17:40:00.097472","created_date":"2025-10-10T00:00:00"}
