{"id":"https://openalex.org/W2077174190","doi":"https://doi.org/10.1090/s0025-5718-98-00993-4","title":"An adaptive strategy for elliptic problems including a posteriori controlled boundary approximation","display_name":"An adaptive strategy for elliptic problems including a posteriori controlled boundary approximation","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W2077174190","doi":"https://doi.org/10.1090/s0025-5718-98-00993-4","mag":"2077174190"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-98-00993-4","is_oa":false,"landing_page_url":"https://doi.org/10.1090/s0025-5718-98-00993-4","pdf_url":null,"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"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011089877","display_name":"Willy D\u00f6rfler","orcid":"https://orcid.org/0000-0003-1558-9236"},"institutions":[{"id":"https://openalex.org/I161046081","display_name":"University of Freiburg","ror":"https://ror.org/0245cg223","country_code":"DE","type":"education","lineage":["https://openalex.org/I161046081"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"W. D\u00f6rfler","raw_affiliation_strings":["Institut f\u00fcr Angewandte Mathematik, Universit\u00e4t Freiburg, Hermann-Herder- Strasse 10, D-79104 Freiburg, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Angewandte Mathematik, Universit\u00e4t Freiburg, Hermann-Herder- Strasse 10, D-79104 Freiburg, Germany","institution_ids":["https://openalex.org/I161046081"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063603168","display_name":"Martin Rumpf","orcid":"https://orcid.org/0000-0001-6049-9390"},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"M. Rumpf","raw_affiliation_strings":["Institut f\u00c3\u00bcr Angewandte Mathematik, Universit\u00c3\u00a4t Bonn, Wegelerstrasse 6, D-52115 Bonn, Germany","Institut f\u00fcr Angewandte Mathematik, Universit\u00e4t Bonn, Wegelerstrasse 6, D-52115 Bonn, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00c3\u00bcr Angewandte Mathematik, Universit\u00c3\u00a4t Bonn, Wegelerstrasse 6, D-52115 Bonn, Germany","institution_ids":["https://openalex.org/I135140700"]},{"raw_affiliation_string":"Institut f\u00fcr Angewandte Mathematik, Universit\u00e4t Bonn, Wegelerstrasse 6, D-52115 Bonn, Germany","institution_ids":["https://openalex.org/I135140700"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5011089877"],"corresponding_institution_ids":["https://openalex.org/I161046081"],"apc_list":null,"apc_paid":null,"fwci":3.1962,"has_fulltext":false,"cited_by_count":50,"citation_normalized_percentile":{"value":0.9154823,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"67","issue":"224","first_page":"1361","last_page":"1382"},"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":0.9998000264167786,"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":0.9998000264167786,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7424535751342773},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6021671295166016},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5792335271835327},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5315544009208679},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5184016227722168},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5046590566635132},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.4458009600639343},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4365420639514923},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4350847005844116},{"id":"https://openalex.org/keywords/adaptive-mesh-refinement","display_name":"Adaptive mesh refinement","score":0.4343872666358948},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22304007411003113},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.07074892520904541}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7424535751342773},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6021671295166016},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5792335271835327},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5315544009208679},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5184016227722168},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5046590566635132},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.4458009600639343},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4365420639514923},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4350847005844116},{"id":"https://openalex.org/C131053463","wikidata":"https://www.wikidata.org/wiki/Q4680751","display_name":"Adaptive mesh refinement","level":2,"score":0.4343872666358948},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22304007411003113},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.07074892520904541},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/s0025-5718-98-00993-4","is_oa":false,"landing_page_url":"https://doi.org/10.1090/s0025-5718-98-00993-4","pdf_url":null,"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:oai:CiteSeerX.psu:10.1.1.192.4796","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.192.4796","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/1998-67-224/S0025-5718-98-00993-4/S0025-5718-98-00993-4.pdf","raw_type":"text"},{"id":"pmh:oai:freidok.uni-freiburg.de:21129","is_oa":false,"landing_page_url":"https://freidok.uni-freiburg.de/data/21129","pdf_url":null,"source":{"id":"https://openalex.org/S4306401057","display_name":"FreiDok plus (Universit\u00e4tsbibliothek Freiburg)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I161046081","host_organization_name":"University of Freiburg","host_organization_lineage":["https://openalex.org/I161046081"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics of Computation. - 67, 224 (1998) , 1361-1383, ISSN: 0025-5718","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1562286121","https://openalex.org/W1597209545","https://openalex.org/W1980604930","https://openalex.org/W1985629301","https://openalex.org/W1986979441","https://openalex.org/W1989594010","https://openalex.org/W1994336408","https://openalex.org/W2006122675","https://openalex.org/W2009985306","https://openalex.org/W2027126956","https://openalex.org/W2039924562","https://openalex.org/W2041523977","https://openalex.org/W2071036364","https://openalex.org/W2075330220","https://openalex.org/W2076458295","https://openalex.org/W2116696529","https://openalex.org/W2124214067","https://openalex.org/W2137568470","https://openalex.org/W2150438822","https://openalex.org/W2167557857","https://openalex.org/W2199169705","https://openalex.org/W2225162326","https://openalex.org/W2615216662","https://openalex.org/W3147515309","https://openalex.org/W4205692696","https://openalex.org/W4232421488","https://openalex.org/W4245007249"],"related_works":["https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W1864774435","https://openalex.org/W946352265","https://openalex.org/W3020787026","https://openalex.org/W2334479858","https://openalex.org/W2799209613","https://openalex.org/W1971388572","https://openalex.org/W1507702947","https://openalex.org/W2362625355"],"abstract_inverted_index":{"We":[0],"derive":[1],"a":[2,28,49,95,100,120,143,149,161,165],"posteriori":[3,54,162],"error":[4,55,117,134],"estimates":[5,56,163],"for":[6],"the":[7,38,41,60,64,86,92,106,109,113,116,129,132,154,156,160,178],"approximation":[8,152],"of":[9,40,85,94,108,112,128,153,159],"linear":[10],"elliptic":[11],"problems":[12],"on":[13,27,37,48,115,169],"domains":[14],"with":[15],"piecewise":[16],"smooth":[17],"boundary.":[18],"The":[19,139],"numerical":[20],"solution":[21],"is":[22,46,89,102,135],"assumed":[23],"to":[24,104,147],"be":[25,182],"defined":[26],"Finite":[29],"Element":[30],"mesh,":[31],"whose":[32],"boundary":[33,39,97],"vertices":[34],"are":[35,57],"located":[36],"continuous":[42],"problem.":[43],"No":[44],"assumption":[45],"made":[47],"geometrically":[50],"fitting":[51],"shape.":[52],"A":[53],"given":[58],"in":[59,91],"energy":[61],"norm":[62],"and":[63,83,164],"<inline-formula":[65],"content-type=\"math/mathml\">":[66],"<mml:math":[67],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[68],"alttext=\"upper":[69],"L":[70],"squared\">":[71],"<mml:semantics>":[72],"<mml:msup>":[73],"<mml:mi>L</mml:mi>":[74],"<mml:mn>2</mml:mn>":[75],"</mml:msup>":[76],"<mml:annotation":[77],"encoding=\"application/x-tex\">L^2</mml:annotation>":[78],"</mml:semantics>":[79],"</mml:math>":[80],"</inline-formula>":[81],"-norm,":[82],"efficiency":[84],"adaptive":[87],"algorithm":[88,141],"proved":[90],"case":[93],"saturated":[96],"approximation.":[98],"Furthermore,":[99],"strategy":[101],"presented":[103,140],"compute":[105],"effect":[107],"non-discretized":[110],"part":[111],"domain":[114],"starting":[118],"from":[119],"coarse":[121],"mesh.":[122],"This":[123],"especially":[124],"implies":[125],"that":[126,175],"parts":[127],"domain,":[130],"where":[131],"measured":[133],"small,":[136],"stay":[137],"non-discretized.":[138],"includes":[142],"stable":[144],"path":[145],"following":[146],"supply":[148],"sufficient":[150],"polygonal":[151],"boundary,":[155],"reliable":[157],"computation":[158],"mesh":[166],"adaptation":[167],"based":[168],"Delaunay":[170],"techniques.":[171],"Numerical":[172],"examples":[173],"illustrate":[174],"errors":[176],"outside":[177],"initial":[179],"discretization":[180],"will":[181],"detected.":[183]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}