{"id":"https://openalex.org/W1971518097","doi":"https://doi.org/10.1137/130940736","title":"An Implicit Midpoint Spectral Approximation of Nonlocal Cahn--Hilliard Equations","display_name":"An Implicit Midpoint Spectral Approximation of Nonlocal Cahn--Hilliard Equations","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W1971518097","doi":"https://doi.org/10.1137/130940736","mag":"1971518097"},"language":"en","primary_location":{"id":"doi:10.1137/130940736","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130940736","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013022790","display_name":"Barbora Bene\u0161ov\u00e1","orcid":"https://orcid.org/0000-0002-6083-247X"},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Barbora Bene\u0161ov\u00e1","raw_affiliation_strings":["Department of Mathematics I, RWTH Aachen University, D-52056 Aachen, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics I, RWTH Aachen University, D-52056 Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017799655","display_name":"Christof Melcher","orcid":"https://orcid.org/0000-0002-0535-2449"},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Christof Melcher","raw_affiliation_strings":["Department of Mathematics I, RWTH Aachen University, D-52056 Aachen, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics I, RWTH Aachen University, D-52056 Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064002486","display_name":"Endre S\u00fcli","orcid":"https://orcid.org/0000-0002-0812-6105"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Endre S\u00fcli","raw_affiliation_strings":["Mathematical Institute, University of Oxford, 24-29 St. Giles, Oxford OX1 3LB, United Kingdom"],"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Oxford, 24-29 St. Giles, Oxford OX1 3LB, United Kingdom","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5017799655"],"corresponding_institution_ids":["https://openalex.org/I887968799"],"apc_list":null,"apc_paid":null,"fwci":0.7148,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.66934612,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"52","issue":"3","first_page":"1466","last_page":"1496"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9941999912261963,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.9380538463592529},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8812299966812134},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.6701303124427795},{"id":"https://openalex.org/keywords/midpoint","display_name":"Midpoint","score":0.6570451855659485},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6154919266700745},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5456564426422119},{"id":"https://openalex.org/keywords/discretization-error","display_name":"Discretization error","score":0.528242290019989},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.517561137676239},{"id":"https://openalex.org/keywords/temporal-discretization","display_name":"Temporal discretization","score":0.5124009251594543},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4876440763473511},{"id":"https://openalex.org/keywords/midpoint-method","display_name":"Midpoint method","score":0.4753310978412628},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4721517562866211},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1953202486038208}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.9380538463592529},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8812299966812134},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6701303124427795},{"id":"https://openalex.org/C34130140","wikidata":"https://www.wikidata.org/wiki/Q1645406","display_name":"Midpoint","level":2,"score":0.6570451855659485},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6154919266700745},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5456564426422119},{"id":"https://openalex.org/C126148662","wikidata":"https://www.wikidata.org/wiki/Q3890355","display_name":"Discretization error","level":3,"score":0.528242290019989},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.517561137676239},{"id":"https://openalex.org/C2778327290","wikidata":"https://www.wikidata.org/wiki/Q17146496","display_name":"Temporal discretization","level":3,"score":0.5124009251594543},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4876440763473511},{"id":"https://openalex.org/C85807060","wikidata":"https://www.wikidata.org/wiki/Q17103851","display_name":"Midpoint method","level":2,"score":0.4753310978412628},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4721517562866211},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1953202486038208},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/130940736","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130940736","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:CiteSeerX.psu:10.1.1.460.7036","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.460.7036","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://people.maths.ox.ac.uk/suli/benesova_melcher_suli_2013.pdf","raw_type":"text"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:122bbeab-86f5-4cda-ad8e-dea62cee9c60","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:122bbeab-86f5-4cda-ad8e-dea62cee9c60","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symplectic Elements at Oxford","raw_type":"Journal article"},{"id":"pmh:oai:publications.rwth-aachen.de:445237","is_oa":false,"landing_page_url":"https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-088207%22","pdf_url":null,"source":{"id":"https://openalex.org/S4306401362","display_name":"RWTH Publications (RWTH Aachen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887968799","host_organization_name":"RWTH Aachen University","host_organization_lineage":["https://openalex.org/I887968799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM journal on numerical analysis 52(3), 1466-1496 (2014). doi:10.1137/130940736","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.46000000834465027}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W76609326","https://openalex.org/W114707485","https://openalex.org/W1529293474","https://openalex.org/W1594665187","https://openalex.org/W1975538793","https://openalex.org/W1987377268","https://openalex.org/W1992445851","https://openalex.org/W2014292079","https://openalex.org/W2019746265","https://openalex.org/W2032257836","https://openalex.org/W2044966729","https://openalex.org/W2046528357","https://openalex.org/W2051078634","https://openalex.org/W2075085615","https://openalex.org/W2077028260","https://openalex.org/W2086147404","https://openalex.org/W2098973108","https://openalex.org/W2120235449","https://openalex.org/W2151733572","https://openalex.org/W2158598889","https://openalex.org/W4230344563"],"related_works":["https://openalex.org/W2072226187","https://openalex.org/W2391598905","https://openalex.org/W2330791370","https://openalex.org/W37565017","https://openalex.org/W2357395917","https://openalex.org/W2055023320","https://openalex.org/W3091779247","https://openalex.org/W2391440809","https://openalex.org/W2626449361","https://openalex.org/W1485125211"],"abstract_inverted_index":{"The":[0,16,39,72],"paper":[1],"is":[2,19,31],"concerned":[3],"with":[4,33,53],"the":[5,22,36,56,64,68,76,84,90,96,99,105],"convergence":[6],"analysis":[7],"of":[8,41,67,78,98,104],"a":[9,27],"numerical":[10,42,79],"method":[11],"for":[12],"nonlocal":[13],"Cahn--Hilliard":[14],"equations.":[15],"temporal":[17],"discretization":[18,30,57,107],"based":[20],"on":[21,63,75,95],"implicit":[23],"midpoint":[24],"rule":[25],"and":[26,59],"Fourier":[28],"spectral":[29],"used":[32],"respect":[34,54],"to":[35,46,55,110],"spatial":[37,106],"variables.":[38],"sequence":[40,77],"approximations":[43],"in":[44,49,89,102],"shown":[45],"be":[47,111],"bounded":[48],"various":[50],"norms,":[51],"uniformly":[52],"parameters,":[58],"optimal":[60],"order":[61],"bounds":[62,74,86],"global":[65],"error":[66,85],"scheme":[69],"are":[70],"derived.":[71],"uniform":[73],"solutions":[80],"as":[81,83],"well":[82],"hold":[87],"unconditionally,":[88],"sense":[91],"that":[92],"no":[93],"restriction":[94],"size":[97],"time":[100],"step":[101],"terms":[103],"parameter":[108],"needs":[109],"assumed.":[112]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}