{"id":"https://openalex.org/W2002086758","doi":"https://doi.org/10.1007/s00211-006-0027-0","title":"Pointwise a posteriori error estimates for monotone semi-linear equations","display_name":"Pointwise a posteriori error estimates for monotone semi-linear equations","publication_year":2006,"publication_date":"2006-08-14","ids":{"openalex":"https://openalex.org/W2002086758","doi":"https://doi.org/10.1007/s00211-006-0027-0","mag":"2002086758"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-006-0027-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-006-0027-0","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-508","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040883953","display_name":"Ricardo H. Nochetto","orcid":"https://orcid.org/0009-0002-8895-1144"},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ricardo H. Nochetto","raw_affiliation_strings":["Department of Mathematics and Institute of Physical Science and Technology, University of Maryland, College Park, MD, 20742, USA","Department of Mathematics and Institute of Physical Science and Technology, University of Maryland, 20742, College Park, MD, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Institute of Physical Science and Technology, University of Maryland, College Park, MD, 20742, USA","institution_ids":["https://openalex.org/I66946132"]},{"raw_affiliation_string":"Department of Mathematics and Institute of Physical Science and Technology, University of Maryland, 20742, College Park, MD, USA#TAB#","institution_ids":["https://openalex.org/I66946132"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008347776","display_name":"Alfred Schmidt","orcid":"https://orcid.org/0000-0003-2363-5378"},"institutions":[{"id":"https://openalex.org/I180437899","display_name":"University of Bremen","ror":"https://ror.org/04ers2y35","country_code":"DE","type":"education","lineage":["https://openalex.org/I180437899"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Alfred Schmidt","raw_affiliation_strings":["Zentrum f\u00fcr Technomathematik,Fachbereich 3 Mathematik und Informatik, Universit\u00e4t Bremen, Postfach 33 04 40, 28334, Bremen, Germany","Zentrum f\u00fcr Technomathematik,Fachbereich 3 Mathematik und Informatik, Universit\u00e4t Bremen, Postfach 33 04 40, 28334, Bremen, MD, Germany#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Zentrum f\u00fcr Technomathematik,Fachbereich 3 Mathematik und Informatik, Universit\u00e4t Bremen, Postfach 33 04 40, 28334, Bremen, Germany","institution_ids":["https://openalex.org/I180437899"]},{"raw_affiliation_string":"Zentrum f\u00fcr Technomathematik,Fachbereich 3 Mathematik und Informatik, Universit\u00e4t Bremen, Postfach 33 04 40, 28334, Bremen, MD, Germany#TAB#","institution_ids":["https://openalex.org/I180437899"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111621776","display_name":"Kunibert G. Siebert","orcid":null},"institutions":[{"id":"https://openalex.org/I119916105","display_name":"Augsburg University","ror":"https://ror.org/057ewhh68","country_code":"US","type":"education","lineage":["https://openalex.org/I119916105"]},{"id":"https://openalex.org/I179225836","display_name":"University of Augsburg","ror":"https://ror.org/03p14d497","country_code":"DE","type":"education","lineage":["https://openalex.org/I179225836"]}],"countries":["DE","US"],"is_corresponding":false,"raw_author_name":"Kunibert G. Siebert","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Universit\u00e4t Augsburg, Universit\u00e4tsstrasse 14, 86159, Augsburg, Germany","Institut f\u00fcr Mathematik, Universit\u00e4t Augsburg, Postfach 33 04 40, Universit\u00e4tsstrasse 14, 86159, Augsburg, MD, Germany#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Universit\u00e4t Augsburg, Universit\u00e4tsstrasse 14, 86159, Augsburg, Germany","institution_ids":["https://openalex.org/I179225836"]},{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Universit\u00e4t Augsburg, Postfach 33 04 40, Universit\u00e4tsstrasse 14, 86159, Augsburg, MD, Germany#TAB#","institution_ids":["https://openalex.org/I119916105"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073393258","display_name":"Andreas Veeser","orcid":"https://orcid.org/0000-0002-2152-2911"},"institutions":[{"id":"https://openalex.org/I189158943","display_name":"University of Milan","ror":"https://ror.org/00wjc7c48","country_code":"IT","type":"education","lineage":["https://openalex.org/I189158943"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Andreas Veeser","raw_affiliation_strings":["Dipartimento di Matematica, Universit\u00e0 degli Studi di Milano, Via C. Saldini 50, 20133, Milano, Italy","Dipartimento di Matematica, Universit\u00e0 degli Studi di Milano, Postfach 33 04 40, Via C. Saldini 50, 20133, Milano, MD, Italy#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Universit\u00e0 degli Studi di Milano, Via C. Saldini 50, 20133, Milano, Italy","institution_ids":["https://openalex.org/I189158943"]},{"raw_affiliation_string":"Dipartimento di Matematica, Universit\u00e0 degli Studi di Milano, Postfach 33 04 40, Via C. Saldini 50, 20133, Milano, MD, Italy#TAB#","institution_ids":["https://openalex.org/I189158943"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5040883953"],"corresponding_institution_ids":["https://openalex.org/I66946132"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":2.2218,"has_fulltext":false,"cited_by_count":49,"citation_normalized_percentile":{"value":0.86093673,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"104","issue":"4","first_page":"515","last_page":"538"},"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":0.9998999834060669,"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":0.9998999834060669,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9973000288009644,"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":0.9959999918937683,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8701988458633423},{"id":"https://openalex.org/keywords/pointwise","display_name":"Pointwise","score":0.7835378646850586},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.6787933111190796},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6396241784095764},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5648972392082214},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.5481706261634827},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5440555810928345},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5325355529785156},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5207797884941101},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.519360363483429},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4960995614528656},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4421970546245575},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3272314667701721},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09846833348274231}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8701988458633423},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.7835378646850586},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6787933111190796},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6396241784095764},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5648972392082214},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.5481706261634827},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5440555810928345},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5325355529785156},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5207797884941101},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.519360363483429},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4960995614528656},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4421970546245575},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3272314667701721},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09846833348274231},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s00211-006-0027-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-006-0027-0","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},{"id":"pmh:oai:aleph.bib-bvb.de:BVB01-013206605","is_oa":false,"landing_page_url":"https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/deliver/index/docId/71/file/monotone.pdf","pdf_url":"https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/deliver/index/docId/71/file/monotone.pdf","source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"software, multimedia"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.158.7439","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.158.7439","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.umd.edu/~rhn/papers/pdf/semilinear.pdf","raw_type":"text"},{"id":"pmh:oai:uni-augsburg.opus-bayern.de:34969","is_oa":false,"landing_page_url":"https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/34969","pdf_url":null,"source":{"id":"https://openalex.org/S4306400930","display_name":"OPUS (Augsburg University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119916105","host_organization_name":"Augsburg University","host_organization_lineage":["https://openalex.org/I119916105"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"},{"id":"pmh:oai:uni-augsburg.opus-bayern.de:71","is_oa":true,"landing_page_url":"https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-508","pdf_url":null,"source":{"id":"https://openalex.org/S4306400930","display_name":"OPUS (Augsburg University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119916105","host_organization_name":"Augsburg University","host_organization_lineage":["https://openalex.org/I119916105"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"preprint"}],"best_oa_location":{"id":"pmh:oai:uni-augsburg.opus-bayern.de:71","is_oa":true,"landing_page_url":"https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-508","pdf_url":null,"source":{"id":"https://openalex.org/S4306400930","display_name":"OPUS (Augsburg University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119916105","host_organization_name":"Augsburg University","host_organization_lineage":["https://openalex.org/I119916105"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"preprint"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320875","display_name":"Deutscher Akademischer Austauschdienst","ror":"https://ror.org/039djdh30"},{"id":"https://openalex.org/F4320321873","display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","ror":"https://ror.org/0166hxq48"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W189799848","https://openalex.org/W1488071155","https://openalex.org/W1492326914","https://openalex.org/W1516681311","https://openalex.org/W1582688509","https://openalex.org/W1586623601","https://openalex.org/W1866311589","https://openalex.org/W1979296656","https://openalex.org/W1989594010","https://openalex.org/W1989665919","https://openalex.org/W1995404822","https://openalex.org/W1996672299","https://openalex.org/W2011077519","https://openalex.org/W2012495675","https://openalex.org/W2036442213","https://openalex.org/W2039745296","https://openalex.org/W2041523977","https://openalex.org/W2044627846","https://openalex.org/W2069048447","https://openalex.org/W2071036364","https://openalex.org/W2090056676","https://openalex.org/W2090963365","https://openalex.org/W2135623248","https://openalex.org/W2505585705","https://openalex.org/W2569670394","https://openalex.org/W2597139510","https://openalex.org/W3021722416","https://openalex.org/W4206230545","https://openalex.org/W4246649419","https://openalex.org/W4299512035"],"related_works":["https://openalex.org/W2264690077","https://openalex.org/W1982256708","https://openalex.org/W1976435035","https://openalex.org/W2532103528","https://openalex.org/W1807403118","https://openalex.org/W1984379032","https://openalex.org/W1976468712","https://openalex.org/W2148982133","https://openalex.org/W2084203569","https://openalex.org/W1985257086"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2025-10-10T00:00:00"}
