{"id":"https://openalex.org/W2078598047","doi":"https://doi.org/10.1007/s10208-014-9238-4","title":"On a Full Discretisation for Nonlinear Second-Order Evolution Equations with Monotone Damping: Construction, Convergence, and Error Estimates","display_name":"On a Full Discretisation for Nonlinear Second-Order Evolution Equations with Monotone Damping: Construction, Convergence, and Error Estimates","publication_year":2015,"publication_date":"2015-01-05","ids":{"openalex":"https://openalex.org/W2078598047","doi":"https://doi.org/10.1007/s10208-014-9238-4","mag":"2078598047"},"language":"en","primary_location":{"id":"doi:10.1007/s10208-014-9238-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-014-9238-4","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":true,"oa_status":"green","oa_url":"https://www.research.ed.ac.uk/en/publications/4974358c-009d-46f6-81c9-4c0229fa758c","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085447239","display_name":"Etienne Emmrich","orcid":"https://orcid.org/0000-0001-9869-0334"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Etienne Emmrich","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Technische Universit\u00e4t Berlin, Stra\u00dfe des 17. Juni 136, 10623, Berlin, Germany","Institut f\u00fcr Mathematik, Technische Universit\u00e4t Berlin, Berlin, Germany 10623#TAB#"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Technische Universit\u00e4t Berlin, Stra\u00dfe des 17. Juni 136, 10623, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]},{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Technische Universit\u00e4t Berlin, Berlin, Germany 10623#TAB#","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086639645","display_name":"David \u0160i\u0161ka","orcid":"https://orcid.org/0000-0002-3474-5719"},"institutions":[{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]},{"id":"https://openalex.org/I4210117017","display_name":"Maxwell Institute for Mathematical Sciences","ror":"https://ror.org/02tsqtg57","country_code":"GB","type":"facility","lineage":["https://openalex.org/I32062511","https://openalex.org/I4210117017","https://openalex.org/I98677209"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"David \u0160i\u0161ka","raw_affiliation_strings":["School of Mathematical Sciences, University of Edinburgh, King\u2019s Buildings, Mayfield Road, Edinburgh, EH9 3JZ, UK","School of Mathematical Sciences, University of Edinburgh, Edinburgh, UK EH9 3JZ#TAB#"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Edinburgh, King\u2019s Buildings, Mayfield Road, Edinburgh, EH9 3JZ, UK","institution_ids":["https://openalex.org/I98677209","https://openalex.org/I4210117017"]},{"raw_affiliation_string":"School of Mathematical Sciences, University of Edinburgh, Edinburgh, UK EH9 3JZ#TAB#","institution_ids":["https://openalex.org/I98677209"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111586019","display_name":"Mechthild Thalhammer","orcid":null},"institutions":[{"id":"https://openalex.org/I190249584","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659","country_code":"AT","type":"education","lineage":["https://openalex.org/I190249584"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Mechthild Thalhammer","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Leopold-Franzens-Universit\u00e4t Innsbruck, Technikerstra\u00dfe 13/VII, 6020, Innsbruck, Austria","Institut f\u00fcr Mathematik, Leopold-Franzens-Universit\u00e4t Innsbruck, Innsbruck, Austria 6020#TAB#"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Leopold-Franzens-Universit\u00e4t Innsbruck, Technikerstra\u00dfe 13/VII, 6020, Innsbruck, Austria","institution_ids":["https://openalex.org/I190249584"]},{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Leopold-Franzens-Universit\u00e4t Innsbruck, Innsbruck, Austria 6020#TAB#","institution_ids":["https://openalex.org/I190249584"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5085447239"],"corresponding_institution_ids":["https://openalex.org/I4577782"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.7276,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.74322058,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"15","issue":"6","first_page":"1653","last_page":"1701"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9998000264167786,"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/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/T10514","display_name":"Numerical methods in engineering","score":0.9995999932289124,"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":0.8583464622497559},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7842807769775391},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6130549311637878},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.5511361360549927},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5438341498374939},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5376431345939636},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.48908787965774536},{"id":"https://openalex.org/keywords/strongly-monotone","display_name":"Strongly monotone","score":0.44662198424339294},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.43796342611312866},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43414849042892456},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4284582734107971},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.3814420700073242},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12776631116867065}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8583464622497559},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7842807769775391},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6130549311637878},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5511361360549927},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5438341498374939},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5376431345939636},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.48908787965774536},{"id":"https://openalex.org/C12715386","wikidata":"https://www.wikidata.org/wiki/Q7624691","display_name":"Strongly monotone","level":3,"score":0.44662198424339294},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.43796342611312866},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43414849042892456},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4284582734107971},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.3814420700073242},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12776631116867065},{"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10208-014-9238-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-014-9238-4","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"},{"id":"pmh:oai:pure.ed.ac.uk:openaire/4974358c-009d-46f6-81c9-4c0229fa758c","is_oa":true,"landing_page_url":"https://www.research.ed.ac.uk/en/publications/4974358c-009d-46f6-81c9-4c0229fa758c","pdf_url":null,"source":{"id":"https://openalex.org/S4406922455","display_name":"Edinburgh Research Explorer","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Emmrich, E, Siska, D & Thalhammer, M 2015, 'On a Full Discretisation for Nonlinear Second-Order Evolution Equations with Monotone Damping: Construction, Convergence, and Error Estimates', Foundations of Computational Mathematics. https://doi.org/10.1007/s10208-014-9238-4","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:pure.ed.ac.uk:publications/4974358c-009d-46f6-81c9-4c0229fa758c","is_oa":false,"landing_page_url":"http://link.springer.com/article/10.1007/s10208-014-9238-4","pdf_url":null,"source":{"id":"https://openalex.org/S4406922455","display_name":"Edinburgh Research Explorer","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":"","raw_type":""}],"best_oa_location":{"id":"pmh:oai:pure.ed.ac.uk:openaire/4974358c-009d-46f6-81c9-4c0229fa758c","is_oa":true,"landing_page_url":"https://www.research.ed.ac.uk/en/publications/4974358c-009d-46f6-81c9-4c0229fa758c","pdf_url":null,"source":{"id":"https://openalex.org/S4406922455","display_name":"Edinburgh Research Explorer","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Emmrich, E, Siska, D & Thalhammer, M 2015, 'On a Full Discretisation for Nonlinear Second-Order Evolution Equations with Monotone Damping: Construction, Convergence, and Error Estimates', Foundations of Computational Mathematics. https://doi.org/10.1007/s10208-014-9238-4","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W334868982","https://openalex.org/W588153840","https://openalex.org/W1486457939","https://openalex.org/W1525219438","https://openalex.org/W1545761024","https://openalex.org/W1555674425","https://openalex.org/W1565460255","https://openalex.org/W1589236075","https://openalex.org/W1661219383","https://openalex.org/W1971738560","https://openalex.org/W1971989699","https://openalex.org/W1985544725","https://openalex.org/W1993535719","https://openalex.org/W2005436751","https://openalex.org/W2014595925","https://openalex.org/W2024911286","https://openalex.org/W2038291611","https://openalex.org/W2069733983","https://openalex.org/W2074432051","https://openalex.org/W2076231979","https://openalex.org/W2100511085","https://openalex.org/W2114612290","https://openalex.org/W2115203263","https://openalex.org/W2158070160","https://openalex.org/W2158637629","https://openalex.org/W2318389815","https://openalex.org/W2322620490","https://openalex.org/W2324452751","https://openalex.org/W2334884490","https://openalex.org/W2582171088","https://openalex.org/W2898916015","https://openalex.org/W2903567145","https://openalex.org/W3091814460","https://openalex.org/W3110425021","https://openalex.org/W4230154502","https://openalex.org/W4232082450","https://openalex.org/W4241008512","https://openalex.org/W4252135546","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2951610245","https://openalex.org/W2795079910","https://openalex.org/W1430963189","https://openalex.org/W2052430123","https://openalex.org/W2049901819","https://openalex.org/W1489292980","https://openalex.org/W4319835971","https://openalex.org/W1983437306","https://openalex.org/W1974262772","https://openalex.org/W2094737495"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}