{"id":"https://openalex.org/W2011775793","doi":"https://doi.org/10.1137/060673242","title":"A Convergent Finite Difference Scheme for the Camassa\u2013Holm Equation with General $H^1$ Initial Data","display_name":"A Convergent Finite Difference Scheme for the Camassa\u2013Holm Equation with General $H^1$ Initial Data","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2011775793","doi":"https://doi.org/10.1137/060673242","mag":"2011775793"},"language":"en","primary_location":{"id":"doi:10.1137/060673242","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060673242","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.duo.uio.no/bitstream/10852/10545/1/pm16-06.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052902271","display_name":"Giuseppe Maria Coclite","orcid":"https://orcid.org/0000-0001-6019-4757"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"G. M. Coclite","raw_affiliation_strings":["Dept. of Math./CMA Univ. of Oslo"],"affiliations":[{"raw_affiliation_string":"Dept. of Math./CMA Univ. of Oslo","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034008502","display_name":"Kenneth H. Karlsen","orcid":"https://orcid.org/0000-0003-3375-2084"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"K. H. Karlsen","raw_affiliation_strings":["Dept. of Math./CMA Univ. of Oslo"],"affiliations":[{"raw_affiliation_string":"Dept. of Math./CMA Univ. of Oslo","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081764581","display_name":"Nils Henrik Risebro","orcid":"https://orcid.org/0000-0003-4069-8282"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"N. H. Risebro","raw_affiliation_strings":["Dept. of Math./CMA Univ. of Oslo"],"affiliations":[{"raw_affiliation_string":"Dept. of Math./CMA Univ. of Oslo","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5052902271"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.6536,"has_fulltext":true,"cited_by_count":50,"citation_normalized_percentile":{"value":0.92951066,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"46","issue":"3","first_page":"1554","last_page":"1579"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":1.0,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":1.0,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9944999814033508,"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"}},{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9912999868392944,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.8636361360549927},{"id":"https://openalex.org/keywords/camassa\u2013holm-equation","display_name":"Camassa\u2013Holm equation","score":0.8225685954093933},{"id":"https://openalex.org/keywords/dissipative-system","display_name":"Dissipative system","score":0.7229521870613098},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.5932995676994324},{"id":"https://openalex.org/keywords/central-differencing-scheme","display_name":"Central differencing scheme","score":0.4780578911304474},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.4771365821361542},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45124363899230957},{"id":"https://openalex.org/keywords/finite-difference-scheme","display_name":"Finite difference scheme","score":0.4474338889122009},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.44141292572021484},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4366830289363861},{"id":"https://openalex.org/keywords/finite-difference-coefficient","display_name":"Finite difference coefficient","score":0.3658002018928528},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.14617598056793213},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.07905435562133789},{"id":"https://openalex.org/keywords/integrable-system","display_name":"Integrable system","score":0.06884536147117615},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06098243594169617}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8636361360549927},{"id":"https://openalex.org/C24454023","wikidata":"https://www.wikidata.org/wiki/Q5025006","display_name":"Camassa\u2013Holm equation","level":3,"score":0.8225685954093933},{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.7229521870613098},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.5932995676994324},{"id":"https://openalex.org/C157866214","wikidata":"https://www.wikidata.org/wiki/Q17006341","display_name":"Central differencing scheme","level":5,"score":0.4780578911304474},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.4771365821361542},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45124363899230957},{"id":"https://openalex.org/C2988766672","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference scheme","level":2,"score":0.4474338889122009},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.44141292572021484},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4366830289363861},{"id":"https://openalex.org/C108268861","wikidata":"https://www.wikidata.org/wiki/Q1747602","display_name":"Finite difference coefficient","level":4,"score":0.3658002018928528},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.14617598056793213},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.07905435562133789},{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.06884536147117615},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06098243594169617},{"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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/060673242","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060673242","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:www.duo.uio.no:10852/10545","is_oa":true,"landing_page_url":"http://hdl.handle.net/10852/10545","pdf_url":"https://www.duo.uio.no/bitstream/10852/10545/1/pm16-06.pdf","source":{"id":"https://openalex.org/S4306401717","display_name":"Duo Research Archive (University of Oslo)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184942183","host_organization_name":"University of Oslo","host_organization_lineage":["https://openalex.org/I184942183"],"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":"info:eu-repo/semantics/report"},{"id":"pmh:oai:ricerca.uniba.it:11586/81006","is_oa":false,"landing_page_url":"http://hdl.handle.net/11586/81006","pdf_url":null,"source":{"id":"https://openalex.org/S4377196296","display_name":"CINECA IRIS Institutional Research Information System (University of Bari Aldo Moro)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I5561750","host_organization_name":"University of Bari Aldo Moro","host_organization_lineage":["https://openalex.org/I5561750"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:www.duo.uio.no:10852/10545","is_oa":true,"landing_page_url":"http://hdl.handle.net/10852/10545","pdf_url":"https://www.duo.uio.no/bitstream/10852/10545/1/pm16-06.pdf","source":{"id":"https://openalex.org/S4306401717","display_name":"Duo Research Archive (University of Oslo)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184942183","host_organization_name":"University of Oslo","host_organization_lineage":["https://openalex.org/I184942183"],"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":"info:eu-repo/semantics/report"},"sustainable_development_goals":[{"display_name":"Affordable and clean energy","score":0.47999998927116394,"id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320323299","display_name":"Norges Forskningsr\u00e5d","ror":"https://ror.org/00epmv149"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2011775793.pdf","grobid_xml":"https://content.openalex.org/works/W2011775793.grobid-xml"},"referenced_works_count":40,"referenced_works":["https://openalex.org/W1492711015","https://openalex.org/W1551335708","https://openalex.org/W1555627060","https://openalex.org/W1562293606","https://openalex.org/W1887903210","https://openalex.org/W1964630003","https://openalex.org/W1968058451","https://openalex.org/W1979571344","https://openalex.org/W1979855427","https://openalex.org/W1981246612","https://openalex.org/W1988923030","https://openalex.org/W1989006082","https://openalex.org/W1992001246","https://openalex.org/W1995410519","https://openalex.org/W1996626681","https://openalex.org/W1999881016","https://openalex.org/W2003212506","https://openalex.org/W2015363211","https://openalex.org/W2017787487","https://openalex.org/W2026031976","https://openalex.org/W2027471184","https://openalex.org/W2046078856","https://openalex.org/W2052443792","https://openalex.org/W2053977972","https://openalex.org/W2054744677","https://openalex.org/W2062619586","https://openalex.org/W2064355804","https://openalex.org/W2069222964","https://openalex.org/W2084217855","https://openalex.org/W2086424643","https://openalex.org/W2087328884","https://openalex.org/W2095224654","https://openalex.org/W2116836540","https://openalex.org/W2122794051","https://openalex.org/W2133286929","https://openalex.org/W2143631463","https://openalex.org/W2152015450","https://openalex.org/W2162550557","https://openalex.org/W2168021114","https://openalex.org/W3009347843"],"related_works":["https://openalex.org/W2034710653","https://openalex.org/W2374957748","https://openalex.org/W2369663565","https://openalex.org/W2356196324","https://openalex.org/W2034249681","https://openalex.org/W2384782458","https://openalex.org/W2370641521","https://openalex.org/W4231701430","https://openalex.org/W2375410388","https://openalex.org/W2011206855"],"abstract_inverted_index":{"We":[0,35],"suggest":[1],"a":[2,31,46],"finite":[3],"dfference":[4],"scheme":[5,22,40],"for":[6],"the":[7,20,38,51],"Camassa\u2013Holm":[8,52],"equation":[9],"that":[10,28,37],"can":[11],"handle":[12],"general":[13],"$H^1$":[14,44],"initial":[15],"data.":[16],"The":[17],"form":[18],"of":[19,50],"difference":[21,39],"is":[23],"judiciously":[24],"chosen":[25],"to":[26],"ensure":[27],"it":[29],"satisfies":[30],"total":[32],"energy":[33],"inequality.":[34],"prove":[36],"converges":[41],"strongly":[42],"in":[43],"towards":[45],"dissipative":[47],"weak":[48],"solution":[49],"equation.":[53]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}