{"id":"https://openalex.org/W2072868100","doi":"https://doi.org/10.1007/s00211-008-0192-4","title":"A local least-squares method for solving nonlinear partial differential equations of second order","display_name":"A local least-squares method for solving nonlinear partial differential equations of second order","publication_year":2008,"publication_date":"2008-11-19","ids":{"openalex":"https://openalex.org/W2072868100","doi":"https://doi.org/10.1007/s00211-008-0192-4","mag":"2072868100"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-008-0192-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-008-0192-4","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011607603","display_name":"Pascal Heider","orcid":null},"institutions":[{"id":"https://openalex.org/I180923762","display_name":"University of Cologne","ror":"https://ror.org/00rcxh774","country_code":"DE","type":"education","lineage":["https://openalex.org/I180923762"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Pascal Heider","raw_affiliation_strings":["Mathematisches Institut, Universit\u00e4t zu K\u00f6ln, Weyertal 86-90, 50931, K\u00f6ln, Germany","Universit\u00e4t zu K\u00f6ln, Mathematisches Institut, Weyertal 86\u201090, 50931 K\u00f6ln, Germany"],"affiliations":[{"raw_affiliation_string":"Mathematisches Institut, Universit\u00e4t zu K\u00f6ln, Weyertal 86-90, 50931, K\u00f6ln, Germany","institution_ids":["https://openalex.org/I180923762"]},{"raw_affiliation_string":"Universit\u00e4t zu K\u00f6ln, Mathematisches Institut, Weyertal 86\u201090, 50931 K\u00f6ln, Germany","institution_ids":["https://openalex.org/I180923762"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5011607603"],"corresponding_institution_ids":["https://openalex.org/I180923762"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.6633,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.74094894,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"111","issue":"3","first_page":"351","last_page":"375"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9998999834060669,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9987000226974487,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9983999729156494,"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":0.8391867280006409},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.825180172920227},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6074649095535278},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5723156929016113},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5105444192886353},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5097808241844177},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.46985116600990295},{"id":"https://openalex.org/keywords/discretization-of-continuous-features","display_name":"Discretization of continuous features","score":0.463348925113678},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.45425912737846375},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.4500001072883606},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.44062697887420654},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3826626241207123},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3359222710132599},{"id":"https://openalex.org/keywords/discretization-error","display_name":"Discretization error","score":0.2714608311653137},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09676194190979004}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8391867280006409},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.825180172920227},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6074649095535278},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5723156929016113},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5105444192886353},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5097808241844177},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.46985116600990295},{"id":"https://openalex.org/C105427703","wikidata":"https://www.wikidata.org/wiki/Q665193","display_name":"Discretization of continuous features","level":4,"score":0.463348925113678},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.45425912737846375},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.4500001072883606},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.44062697887420654},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3826626241207123},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3359222710132599},{"id":"https://openalex.org/C126148662","wikidata":"https://www.wikidata.org/wiki/Q3890355","display_name":"Discretization error","level":3,"score":0.2714608311653137},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09676194190979004},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00211-008-0192-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-008-0192-4","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320324811","display_name":"Universit\u00e4t zu K\u00f6ln","ror":"https://ror.org/00rcxh774"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W201035275","https://openalex.org/W647089673","https://openalex.org/W1486164486","https://openalex.org/W1570844572","https://openalex.org/W1597405158","https://openalex.org/W1988744163","https://openalex.org/W2000210554","https://openalex.org/W2018039791","https://openalex.org/W2019180174","https://openalex.org/W2035427988","https://openalex.org/W2044355921","https://openalex.org/W2046335377","https://openalex.org/W2054732436","https://openalex.org/W2062757794","https://openalex.org/W2069776858","https://openalex.org/W2074429597","https://openalex.org/W2088803423","https://openalex.org/W2092011174","https://openalex.org/W2092043736","https://openalex.org/W2094048486","https://openalex.org/W2142136198","https://openalex.org/W2168414272","https://openalex.org/W2254604671","https://openalex.org/W2264065105","https://openalex.org/W2321310861","https://openalex.org/W2330755614","https://openalex.org/W2900335257","https://openalex.org/W4205796455","https://openalex.org/W4233950352","https://openalex.org/W4240596267","https://openalex.org/W4251512373"],"related_works":["https://openalex.org/W4388311650","https://openalex.org/W1974056099","https://openalex.org/W2386077341","https://openalex.org/W563589758","https://openalex.org/W5922282","https://openalex.org/W2954004777","https://openalex.org/W2949638731","https://openalex.org/W2951102138","https://openalex.org/W2064416388","https://openalex.org/W4388482258"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}