{"id":"https://openalex.org/W2010668070","doi":"https://doi.org/10.1007/s10208-013-9183-7","title":"Convergence Analysis of Spatially Adaptive Rothe Methods","display_name":"Convergence Analysis of Spatially Adaptive Rothe Methods","publication_year":2014,"publication_date":"2014-02-18","ids":{"openalex":"https://openalex.org/W2010668070","doi":"https://doi.org/10.1007/s10208-013-9183-7","mag":"2010668070"},"language":"en","primary_location":{"id":"doi:10.1007/s10208-013-9183-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-013-9183-7","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"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":"Foundations of Computational Mathematics","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/A5089341038","display_name":"Petru A. Cioica-Licht","orcid":"https://orcid.org/0000-0003-0308-9779"},"institutions":[{"id":"https://openalex.org/I161103922","display_name":"Philipps University of Marburg","ror":"https://ror.org/01rdrb571","country_code":"DE","type":"education","lineage":["https://openalex.org/I161103922"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Petru A. Cioica","raw_affiliation_strings":["FB Mathematik und Informatik, AG Numerik/Optimierung, Philipps-Universit\u00e4t Marburg, Hans-Meerwein-Strasse, 35032\u00a0, Marburg, Germany","FB Mathematik und Informatik, AG Numerik/Optimierung, Philipps-Universit\u00e4t Marburg, Marburg, Germany 35032#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"FB Mathematik und Informatik, AG Numerik/Optimierung, Philipps-Universit\u00e4t Marburg, Hans-Meerwein-Strasse, 35032\u00a0, Marburg, Germany","institution_ids":["https://openalex.org/I161103922"]},{"raw_affiliation_string":"FB Mathematik und Informatik, AG Numerik/Optimierung, Philipps-Universit\u00e4t Marburg, Marburg, Germany 35032#TAB#","institution_ids":["https://openalex.org/I161103922"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047150999","display_name":"Stephan Dahlke","orcid":"https://orcid.org/0000-0003-0168-7257"},"institutions":[{"id":"https://openalex.org/I161103922","display_name":"Philipps University of Marburg","ror":"https://ror.org/01rdrb571","country_code":"DE","type":"education","lineage":["https://openalex.org/I161103922"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Stephan Dahlke","raw_affiliation_strings":["FB Mathematik und Informatik, AG Numerik/Optimierung, Philipps-Universit\u00e4t Marburg, Hans-Meerwein-Strasse, 35032\u00a0, Marburg, Germany","FB Mathematik und Informatik, AG Numerik/Optimierung, Philipps-Universit\u00e4t Marburg, Marburg, Germany 35032#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"FB Mathematik und Informatik, AG Numerik/Optimierung, Philipps-Universit\u00e4t Marburg, Hans-Meerwein-Strasse, 35032\u00a0, Marburg, Germany","institution_ids":["https://openalex.org/I161103922"]},{"raw_affiliation_string":"FB Mathematik und Informatik, AG Numerik/Optimierung, Philipps-Universit\u00e4t Marburg, Marburg, Germany 35032#TAB#","institution_ids":["https://openalex.org/I161103922"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050914996","display_name":"Nicolas D\u00f6hring","orcid":null},"institutions":[{"id":"https://openalex.org/I153267046","display_name":"University of Kaiserslautern","ror":"https://ror.org/04zrf7b53","country_code":"DE","type":"education","lineage":["https://openalex.org/I153267046"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Nicolas D\u00f6hring","raw_affiliation_strings":["Fachbereich Mathematik, TU Kaiserslautern, Postfach 3049, 67653\u00a0, Kaiserslautern, Germany","Fachbereich Mathematik, TU Kaiserslautern, Kaiserslautern, Germany 67653#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fachbereich Mathematik, TU Kaiserslautern, Postfach 3049, 67653\u00a0, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I153267046"]},{"raw_affiliation_string":"Fachbereich Mathematik, TU Kaiserslautern, Kaiserslautern, Germany 67653#TAB#","institution_ids":["https://openalex.org/I153267046"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000948594","display_name":"Ulrich Friedrich","orcid":null},"institutions":[{"id":"https://openalex.org/I161103922","display_name":"Philipps University of Marburg","ror":"https://ror.org/01rdrb571","country_code":"DE","type":"education","lineage":["https://openalex.org/I161103922"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ulrich Friedrich","raw_affiliation_strings":["FB Mathematik und Informatik, AG Numerik/Optimierung, Philipps-Universit\u00e4t Marburg, Hans-Meerwein-Strasse, 35032\u00a0, Marburg, Germany","FB Mathematik und Informatik, AG Numerik/Optimierung, Philipps-Universit\u00e4t Marburg, Marburg, Germany 35032#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"FB Mathematik und Informatik, AG Numerik/Optimierung, Philipps-Universit\u00e4t Marburg, Hans-Meerwein-Strasse, 35032\u00a0, Marburg, Germany","institution_ids":["https://openalex.org/I161103922"]},{"raw_affiliation_string":"FB Mathematik und Informatik, AG Numerik/Optimierung, Philipps-Universit\u00e4t Marburg, Marburg, Germany 35032#TAB#","institution_ids":["https://openalex.org/I161103922"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045973374","display_name":"Stefan Kinzel","orcid":null},"institutions":[{"id":"https://openalex.org/I161103922","display_name":"Philipps University of Marburg","ror":"https://ror.org/01rdrb571","country_code":"DE","type":"education","lineage":["https://openalex.org/I161103922"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Stefan Kinzel","raw_affiliation_strings":["FB Mathematik und Informatik, AG Numerik/Optimierung, Philipps-Universit\u00e4t Marburg, Hans-Meerwein-Strasse, 35032\u00a0, Marburg, Germany","FB Mathematik und Informatik, AG Numerik/Optimierung, Philipps-Universit\u00e4t Marburg, Marburg, Germany 35032#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"FB Mathematik und Informatik, AG Numerik/Optimierung, Philipps-Universit\u00e4t Marburg, Hans-Meerwein-Strasse, 35032\u00a0, Marburg, Germany","institution_ids":["https://openalex.org/I161103922"]},{"raw_affiliation_string":"FB Mathematik und Informatik, AG Numerik/Optimierung, Philipps-Universit\u00e4t Marburg, Marburg, Germany 35032#TAB#","institution_ids":["https://openalex.org/I161103922"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058512580","display_name":"Felix Lindner","orcid":"https://orcid.org/0000-0002-6439-8930"},"institutions":[{"id":"https://openalex.org/I153267046","display_name":"University of Kaiserslautern","ror":"https://ror.org/04zrf7b53","country_code":"DE","type":"education","lineage":["https://openalex.org/I153267046"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Felix Lindner","raw_affiliation_strings":["Fachbereich Mathematik, TU Kaiserslautern, Postfach 3049, 67653\u00a0, Kaiserslautern, Germany","Fachbereich Mathematik, TU Kaiserslautern, Kaiserslautern, Germany 67653#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fachbereich Mathematik, TU Kaiserslautern, Postfach 3049, 67653\u00a0, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I153267046"]},{"raw_affiliation_string":"Fachbereich Mathematik, TU Kaiserslautern, Kaiserslautern, Germany 67653#TAB#","institution_ids":["https://openalex.org/I153267046"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050159269","display_name":"Thorsten Raasch","orcid":"https://orcid.org/0000-0002-2607-3115"},"institutions":[{"id":"https://openalex.org/I197323543","display_name":"Johannes Gutenberg University Mainz","ror":"https://ror.org/023b0x485","country_code":"DE","type":"education","lineage":["https://openalex.org/I197323543"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Thorsten Raasch","raw_affiliation_strings":["Institut f\u00fcr Mathematik, AG Numerische Mathematik, Johannes Gutenberg-Universit\u00e4t Mainz, Staudingerweg 9, 55099\u00a0, Mainz, Germany","Institut f\u00fcr Mathematik, AG Numerische Mathematik, Johannes Gutenberg-Universit\u00e4t Mainz, Mainz, Germany 55099#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, AG Numerische Mathematik, Johannes Gutenberg-Universit\u00e4t Mainz, Staudingerweg 9, 55099\u00a0, Mainz, Germany","institution_ids":["https://openalex.org/I197323543"]},{"raw_affiliation_string":"Institut f\u00fcr Mathematik, AG Numerische Mathematik, Johannes Gutenberg-Universit\u00e4t Mainz, Mainz, Germany 55099#TAB#","institution_ids":["https://openalex.org/I197323543"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110337597","display_name":"Klaus Ritter","orcid":null},"institutions":[{"id":"https://openalex.org/I153267046","display_name":"University of Kaiserslautern","ror":"https://ror.org/04zrf7b53","country_code":"DE","type":"education","lineage":["https://openalex.org/I153267046"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Klaus Ritter","raw_affiliation_strings":["Fachbereich Mathematik, TU Kaiserslautern, Postfach 3049, 67653\u00a0, Kaiserslautern, Germany","Fachbereich Mathematik, TU Kaiserslautern, Kaiserslautern, Germany 67653#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fachbereich Mathematik, TU Kaiserslautern, Postfach 3049, 67653\u00a0, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I153267046"]},{"raw_affiliation_string":"Fachbereich Mathematik, TU Kaiserslautern, Kaiserslautern, Germany 67653#TAB#","institution_ids":["https://openalex.org/I153267046"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066141763","display_name":"Ren\u00e9 L. Schilling","orcid":"https://orcid.org/0000-0002-7494-048X"},"institutions":[{"id":"https://openalex.org/I78650965","display_name":"Technische Universit\u00e4t Dresden","ror":"https://ror.org/042aqky30","country_code":"DE","type":"education","lineage":["https://openalex.org/I78650965"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ren\u00e9 L. Schilling","raw_affiliation_strings":["Institut f\u00fcr Mathematische Stochastik, TU Dresden, FR Mathematik, 01062\u00a0, Dresden, Germany","Institut f\u00fcr Mathematische Stochastik, TU Dresden, FR Mathematik, Dresden, Germany 01062#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematische Stochastik, TU Dresden, FR Mathematik, 01062\u00a0, Dresden, Germany","institution_ids":["https://openalex.org/I78650965"]},{"raw_affiliation_string":"Institut f\u00fcr Mathematische Stochastik, TU Dresden, FR Mathematik, Dresden, Germany 01062#TAB#","institution_ids":["https://openalex.org/I78650965"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":9,"corresponding_author_ids":["https://openalex.org/A5089341038"],"corresponding_institution_ids":["https://openalex.org/I161103922"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":1.9314,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.8423027,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"14","issue":"5","first_page":"863","last_page":"912"},"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":0.9997000098228455,"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":0.9997000098228455,"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":0.9975000023841858,"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":0.9973000288009644,"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/mathematics","display_name":"Mathematics","score":0.8441697955131531},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7980158925056458},{"id":"https://openalex.org/keywords/integrator","display_name":"Integrator","score":0.6144897937774658},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6125222444534302},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5763505697250366},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5750129222869873},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5073603987693787},{"id":"https://openalex.org/keywords/spacetime","display_name":"Spacetime","score":0.4714440107345581},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.46408745646476746},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4581148028373718},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.42691484093666077},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.41176488995552063},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10502541065216064}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8441697955131531},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7980158925056458},{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.6144897937774658},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6125222444534302},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5763505697250366},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5750129222869873},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5073603987693787},{"id":"https://openalex.org/C130187892","wikidata":"https://www.wikidata.org/wiki/Q133327","display_name":"Spacetime","level":2,"score":0.4714440107345581},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.46408745646476746},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4581148028373718},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.42691484093666077},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.41176488995552063},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10502541065216064},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10208-013-9183-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-013-9183-7","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"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":"Foundations of Computational Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.7599999904632568}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W73070462","https://openalex.org/W75801351","https://openalex.org/W99776242","https://openalex.org/W560409768","https://openalex.org/W590322990","https://openalex.org/W1527296550","https://openalex.org/W1538588718","https://openalex.org/W1539855477","https://openalex.org/W1575147392","https://openalex.org/W1946834781","https://openalex.org/W1965332272","https://openalex.org/W1972883869","https://openalex.org/W1980642013","https://openalex.org/W1985629301","https://openalex.org/W1988406495","https://openalex.org/W1994336408","https://openalex.org/W2010431816","https://openalex.org/W2013283293","https://openalex.org/W2033045446","https://openalex.org/W2034167241","https://openalex.org/W2038626747","https://openalex.org/W2039066931","https://openalex.org/W2039924562","https://openalex.org/W2045050233","https://openalex.org/W2048834141","https://openalex.org/W2060170348","https://openalex.org/W2062728462","https://openalex.org/W2071036364","https://openalex.org/W2072811159","https://openalex.org/W2077956288","https://openalex.org/W2079275676","https://openalex.org/W2082051696","https://openalex.org/W2082621526","https://openalex.org/W2084005055","https://openalex.org/W2084743165","https://openalex.org/W2095219532","https://openalex.org/W2095507168","https://openalex.org/W2095942590","https://openalex.org/W2105129588","https://openalex.org/W2429258439","https://openalex.org/W2575276781","https://openalex.org/W4231428347","https://openalex.org/W4253840677","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2366352762","https://openalex.org/W2613964090","https://openalex.org/W2380425739","https://openalex.org/W2081322886","https://openalex.org/W2349324463","https://openalex.org/W1988313539","https://openalex.org/W2029980887","https://openalex.org/W2027541371","https://openalex.org/W2380535488","https://openalex.org/W2371144154"],"abstract_inverted_index":null,"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-05-03T08:25:01.440150","created_date":"2025-10-10T00:00:00"}