{"id":"https://openalex.org/W7163889666","doi":"https://doi.org/10.48550/arxiv.2606.07164","title":"Numerical Approximation of the stochastic Cahn--Hilliard equation with singular potential","display_name":"Numerical Approximation of the stochastic Cahn--Hilliard equation with singular potential","publication_year":2026,"publication_date":"2026-06-05","ids":{"openalex":"https://openalex.org/W7163889666","doi":"https://doi.org/10.48550/arxiv.2606.07164"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.07164","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.07164","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.07164","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091885680","display_name":"\u013dubom\u00edr Ba\u0148as","orcid":"https://orcid.org/0000-0003-3041-6405"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ba\u0148as, \u013dubom\u00edr","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5138106177","display_name":"Stefan Metzger","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Metzger, Stefan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.3903000056743622,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.3903000056743622,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.33550000190734863,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.07289999723434448,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7724000215530396},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5468999743461609},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.461899995803833},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4415000081062317},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.4399999976158142},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.4343000054359436},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"Numerical stability","score":0.4138000011444092},{"id":"https://openalex.org/keywords/numerical-approximation","display_name":"Numerical approximation","score":0.4025000035762787}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8227999806404114},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7724000215530396},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5468999743461609},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5016999840736389},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.461899995803833},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4415000081062317},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.4399999976158142},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.4343000054359436},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43070000410079956},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.4138000011444092},{"id":"https://openalex.org/C2986878899","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical approximation","level":3,"score":0.4025000035762787},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.3587000072002411},{"id":"https://openalex.org/C55479107","wikidata":"https://www.wikidata.org/wiki/Q97663916","display_name":"Stochastic approximation","level":3,"score":0.35260000824928284},{"id":"https://openalex.org/C135909967","wikidata":"https://www.wikidata.org/wiki/Q4338245","display_name":"Singular solution","level":2,"score":0.3384999930858612},{"id":"https://openalex.org/C39177556","wikidata":"https://www.wikidata.org/wiki/Q7100567","display_name":"Order of accuracy","level":4,"score":0.335999995470047},{"id":"https://openalex.org/C45137528","wikidata":"https://www.wikidata.org/wiki/Q7977966","display_name":"Weak solution","level":2,"score":0.30570000410079956},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.29490000009536743},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.29440000653266907},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.28040000796318054},{"id":"https://openalex.org/C117148685","wikidata":"https://www.wikidata.org/wiki/Q6865376","display_name":"Minimax approximation algorithm","level":2,"score":0.2750999927520752},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.26980000734329224},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.26010000705718994}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.07164","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.07164","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.07164","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.07164","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,19,48,102],"discuss":[1],"the":[2,6,30,45,52,63,78,84,89,96,111,121,124],"numerical":[3,106,113],"approximation":[4,27,53,114],"of":[5,51,62,95,123],"stochastic":[7,65,99],"Cahn--Hilliard":[8,66,100],"equation":[9,67],"with":[10,42],"a":[11,21,59,74],"singular":[12,64,98],"double-obstacle":[13],"potential":[14],"and":[15,32,119],"multiplicative":[16],"conservative":[17,125],"noise.":[18,126],"propose":[20],"regularised":[22,60,79,85,112],"fully":[23],"discrete":[24],"finite":[25],"element":[26],"scheme":[28],"for":[29,54,77],"problem":[31,80],"show":[33,49,82],"that":[34,83],"it":[35],"satisfies":[36],"stability":[37],"estimates":[38],"which":[39],"are":[40],"uniform":[41,75],"respect":[43],"to":[44,73,115],"discretization":[46,56],"parameters.":[47],"convergence":[50],"vanishing":[55],"parameters":[57],"towards":[58,88],"version":[61],"by":[68,104],"monotonicity":[69],"arguments.":[70],"Hence,":[71],"thanks":[72],"$H^1$-estimate":[76],"we":[81,109],"solution":[86,94],"converges":[87],"pathwise":[90],"unique":[91],"probabilistically":[92],"strong":[93],"original":[97],"equation.":[101],"conclude":[103],"presenting":[105],"simulations":[107],"where":[108],"compare":[110],"its":[116],"unregularised":[117],"counterpart":[118],"illustrate":[120],"effect":[122]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-09T00:00:00"}
