{"id":"https://openalex.org/W2810738953","doi":"https://doi.org/10.1090/mcom/3418","title":"Unconditionally energy stable fully discrete schemes for a chemo-repulsion model","display_name":"Unconditionally energy stable fully discrete schemes for a chemo-repulsion model","publication_year":2019,"publication_date":"2019-01-09","ids":{"openalex":"https://openalex.org/W2810738953","doi":"https://doi.org/10.1090/mcom/3418","mag":"2810738953"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3418","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3418","pdf_url":"https://www.ams.org/mcom/2019-88-319/S0025-5718-2019-03418-X/S0025-5718-2019-03418-X.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2019-88-319/S0025-5718-2019-03418-X/S0025-5718-2019-03418-X.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018292728","display_name":"Francisco Guill\u00e9n\u2010Gonz\u00e1lez","orcid":"https://orcid.org/0000-0001-5539-5888"},"institutions":[{"id":"https://openalex.org/I79238269","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24","country_code":"ES","type":"education","lineage":["https://openalex.org/I79238269"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"F. Guill\u00e9n-Gonz\u00e1lez","raw_affiliation_strings":["Departamento de Ecuaciones Diferenciales y An\u00c3\u00a1lisis Num\u00c3\u00a9rico and IMUS, Universidad de Sevilla, Facultad de Matem\u00c3\u00a1ticas, C/ Tarfia, S/N, 41012 Sevilla, Spain","Departamento de Ecuaciones Diferenciales y An\u00e1lisis Num\u00e9rico and IMUS, Universidad de Sevilla, Facultad de Matem\u00e1ticas, C/ Tarfia, S/N, 41012 Sevilla, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Ecuaciones Diferenciales y An\u00c3\u00a1lisis Num\u00c3\u00a9rico and IMUS, Universidad de Sevilla, Facultad de Matem\u00c3\u00a1ticas, C/ Tarfia, S/N, 41012 Sevilla, Spain","institution_ids":["https://openalex.org/I79238269"]},{"raw_affiliation_string":"Departamento de Ecuaciones Diferenciales y An\u00e1lisis Num\u00e9rico and IMUS, Universidad de Sevilla, Facultad de Matem\u00e1ticas, C/ Tarfia, S/N, 41012 Sevilla, Spain","institution_ids":["https://openalex.org/I79238269"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046829965","display_name":"Mar\u00eda \u00c1ngeles Rodr\u00edguez\u2010Bellido","orcid":"https://orcid.org/0000-0002-4561-6437"},"institutions":[{"id":"https://openalex.org/I79238269","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24","country_code":"ES","type":"education","lineage":["https://openalex.org/I79238269"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"M. A. Rodr\u00edguez-Bellido","raw_affiliation_strings":["Departamento de Ecuaciones Diferenciales y An\u00c3\u00a1lisis Num\u00c3\u00a9rico and IMUS, Universidad de Sevilla, Facultad de Matem\u00c3\u00a1ticas, C/ Tarfia, S/N, 41012 Sevilla, Spain","Departamento de Ecuaciones Diferenciales y An\u00e1lisis Num\u00e9rico and IMUS, Universidad de Sevilla, Facultad de Matem\u00e1ticas, C/ Tarfia, S/N, 41012 Sevilla, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Ecuaciones Diferenciales y An\u00c3\u00a1lisis Num\u00c3\u00a9rico and IMUS, Universidad de Sevilla, Facultad de Matem\u00c3\u00a1ticas, C/ Tarfia, S/N, 41012 Sevilla, Spain","institution_ids":["https://openalex.org/I79238269"]},{"raw_affiliation_string":"Departamento de Ecuaciones Diferenciales y An\u00e1lisis Num\u00e9rico and IMUS, Universidad de Sevilla, Facultad de Matem\u00e1ticas, C/ Tarfia, S/N, 41012 Sevilla, Spain","institution_ids":["https://openalex.org/I79238269"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035714622","display_name":"Diego A. Rueda-G\u00f3mez","orcid":"https://orcid.org/0000-0002-3721-1958"},"institutions":[{"id":"https://openalex.org/I115684694","display_name":"Industrial University of Santander","ror":"https://ror.org/00xc1d948","country_code":"CO","type":"education","lineage":["https://openalex.org/I115684694"]}],"countries":["CO"],"is_corresponding":false,"raw_author_name":"D. A. Rueda-G\u00f3mez","raw_affiliation_strings":["Escuela de Matem\u00c3\u00a1ticas, Universidad Industrial de Santander, A.A. 678, Bucaramanga, Colombia","Escuela de Matem\u00e1ticas; Universidad Industrial de Santander; A.A. 678 Bucaramanga Colombia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Escuela de Matem\u00c3\u00a1ticas, Universidad Industrial de Santander, A.A. 678, Bucaramanga, Colombia","institution_ids":["https://openalex.org/I115684694"]},{"raw_affiliation_string":"Escuela de Matem\u00e1ticas; Universidad Industrial de Santander; A.A. 678 Bucaramanga Colombia","institution_ids":["https://openalex.org/I115684694"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0038432,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"88","issue":"319","first_page":"2069","last_page":"2099"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9991000294685364,"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":0.9958999752998352,"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/nabla-symbol","display_name":"Nabla symbol","score":0.940520703792572},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.7497800588607788},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.7436306476593018},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.6588848829269409},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6089581251144409},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5758726596832275},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5183059573173523},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.46281445026397705},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.45244354009628296},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4492258131504059},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.42870888113975525},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4196818768978119},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3937762975692749},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.38053029775619507},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3210568130016327},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1793774962425232},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11878502368927002}],"concepts":[{"id":"https://openalex.org/C54207081","wikidata":"https://www.wikidata.org/wiki/Q937750","display_name":"Nabla symbol","level":3,"score":0.940520703792572},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7497800588607788},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.7436306476593018},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.6588848829269409},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6089581251144409},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5758726596832275},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5183059573173523},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.46281445026397705},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.45244354009628296},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4492258131504059},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.42870888113975525},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4196818768978119},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3937762975692749},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.38053029775619507},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3210568130016327},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1793774962425232},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11878502368927002},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1090/mcom/3418","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3418","pdf_url":"https://www.ams.org/mcom/2019-88-319/S0025-5718-2019-03418-X/S0025-5718-2019-03418-X.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1807.01118","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1807.01118","pdf_url":"https://arxiv.org/pdf/1807.01118","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":null,"raw_type":"text"},{"id":"mag:2810738953","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1807.01118","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:dnet:idus________::a4bc5241a27b8e341aa90856dbd2ea87","is_oa":true,"landing_page_url":"https://idus.us.es/handle//11441/89076","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1807.01118","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1807.01118","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":"article"}],"best_oa_location":{"id":"doi:10.1090/mcom/3418","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3418","pdf_url":"https://www.ams.org/mcom/2019-88-319/S0025-5718-2019-03418-X/S0025-5718-2019-03418-X.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.44999998807907104}],"awards":[{"id":"https://openalex.org/G2265393715","display_name":null,"funder_award_id":"MTM2015-69875-P","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"}],"funders":[{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2810738953.pdf","grobid_xml":"https://content.openalex.org/works/W2810738953.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1604809219","https://openalex.org/W1999604861","https://openalex.org/W2052607781","https://openalex.org/W2077313431","https://openalex.org/W2080055296","https://openalex.org/W2086365560","https://openalex.org/W2091354014","https://openalex.org/W2102952103","https://openalex.org/W2126617016","https://openalex.org/W2134762099","https://openalex.org/W2147156709","https://openalex.org/W2153986075","https://openalex.org/W2156194051","https://openalex.org/W2292972364","https://openalex.org/W2325189417","https://openalex.org/W2562132457","https://openalex.org/W2964350438","https://openalex.org/W6600041127"],"related_works":["https://openalex.org/W2964283182","https://openalex.org/W2789830772","https://openalex.org/W3009325449","https://openalex.org/W3030791699","https://openalex.org/W2792734277","https://openalex.org/W1884644270","https://openalex.org/W3109684313","https://openalex.org/W2885092532","https://openalex.org/W3099205530","https://openalex.org/W3035234576","https://openalex.org/W2522634436","https://openalex.org/W2625328146","https://openalex.org/W2796694886","https://openalex.org/W2962738836","https://openalex.org/W2703856725","https://openalex.org/W3026935255","https://openalex.org/W2472333466","https://openalex.org/W2083154033","https://openalex.org/W2945665580","https://openalex.org/W2950197305"],"abstract_inverted_index":{"This":[0],"work":[1],"is":[2,389],"devoted":[3],"to":[4],"studying":[5],"unconditionally":[6],"energy":[7],"stable":[8],"and":[9,46],"mass-conservative":[10],"numerical":[11],"schemes":[12],"for":[13],"the":[14,43,70,394],"following":[15],"repulsive-productive":[16],"chemotaxis":[17],"model:":[18],"find":[19],"<inline-formula":[20,47,309,349],"content-type=\"math/mathml\">":[21,48,76,310,350],"<mml:math":[22,49,77,311,351],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[23,50,78,312,352],"alttext=\"u":[24],"greater-than-or-equal-to":[25,52],"0\">":[26,53],"<mml:semantics>":[27,54,139,322,358],"<mml:mrow>":[28,55,140,323,359],"<mml:mi>u</mml:mi>":[29,158,166,179,230],"<mml:mo>":[30,57,159,167,174,219,328],"\u2265":[31,58],"</mml:mo>":[32,59,161,169,176,221,330],"<mml:mn>0</mml:mn>":[33,60,188,205,247],"</mml:mrow>":[34,61,256,336,339,365],"<mml:annotation":[35,62,257,340,366],"encoding=\"application/x-tex\">u":[36],"\\geq":[37,64],"0</mml:annotation>":[38,65],"</mml:semantics>":[39,66,302,345,368],"</mml:math>":[40,67,303,346,369],"</inline-formula>":[41,68,347,370],",":[42,69,348],"cell":[44],"density,":[45],"alttext=\"v":[51],"<mml:mi>v</mml:mi>":[56,184,218,226,228],"encoding=\"application/x-tex\">v":[63],"chemical":[71],"concentration,":[72],"such":[73],"that":[74],"<disp-formula":[75],"alttext=\"StartLayout":[79],"Enlarged":[80],"left-brace":[81],"1st":[82],"Row":[83,114],"partial-differential":[84,115],"Subscript":[85,116],"t":[86,109,117,134],"Baseline":[87,118],"u":[88,93,98,128,265,268,290],"minus":[89,94,120],"normal":[90,105,121,130],"upper":[91,106,122,131,314,318],"Delta":[92,123],"nabla":[95,99],"dot":[96],"left-parenthesis":[97],"v":[100,119,124,126,283,286,288],"right-parenthesis":[101],"equals":[102,127,354],"0":[103,111,136],"in":[104,129,305,393],"Omega":[107,132,315],"comma":[108,112,133,137,356],"greater-than":[110,135],"2nd":[113],"plus":[125],"EndLayout\">":[138],"<mml:mo>{</mml:mo>":[141],"<mml:mtable":[142],"align=\"center\"":[143],"columnalign=\"left":[144],"left":[145],"left\"":[146],"rowspacing=\"4pt\"":[147],"columnspacing=\"1em\">":[148],"<mml:mtr>":[149,209],"<mml:mtd>":[150,210],"<mml:msub>":[151,211],"<mml:mi":[152,162,170,180,196,212,222,238,324,334],"mathvariant=\"normal\">":[153,163,171,181,197,213,223,239,325],"\u2202":[154,214],"</mml:mi>":[155,165,173,183,199,215,225,241,327],"<mml:mi>t</mml:mi>":[156,203,216,245],"</mml:msub>":[157,217],"\u2212":[160,168,220],"\u0394":[164,224],"\u2207":[172,182],"\u22c5":[175],"<mml:mo":[177,185,252],"stretchy=\"false\">(</mml:mo>":[178],"stretchy=\"false\">)</mml:mo>":[186],"<mml:mo>=</mml:mo>":[187,229,361],"<mml:mtext>":[189,191,194,201,231,233,236,243],"</mml:mtext>":[190,192,195,202,232,234,237,244],"<mml:mtext>in</mml:mtext>":[193,235],"\u03a9":[198,240,326],"<mml:mo>,</mml:mo>":[200,206,242,248,363],"<mml:mo>&gt;</mml:mo>":[204,246],"</mml:mtd>":[207,249],"</mml:mtr>":[208,250],"<mml:mo>+</mml:mo>":[227],"</mml:mtable>":[251],"fence=\"true\"":[253],"stretchy=\"true\"":[254],"symmetric=\"true\"/>":[255],"encoding=\"application/x-tex\">\\begin{equation*}":[258],"\\left":[259],"\\{":[260],"\\begin":[261],"{array}":[262],"[c]{lll}\\partial":[263],"_t":[264,282],"-":[266,269,284],"\\Delta":[267,285],"\\nabla":[270],"\\cdot":[271],"(u\\nabla":[272],"v)=0":[273],"\\":[274,275,291,292],"\\text":[276,293],"{in}\\":[277,294],"\\Omega":[278,295],",\\":[279,296],"t&gt;0,\\\\":[280],"\\partial":[281],"+":[287],"=":[289],"t&gt;0,":[297],"\\end{array}":[298],"\\right":[299],".":[300,371],"\\end{equation*}</mml:annotation>":[301],"</disp-formula>":[304],"a":[306,374,390],"bounded":[307],"domain":[308],"alttext=\"normal":[313],"subset-of-or-equal-to":[316],"double-struck":[317],"R":[319],"Superscript":[320],"d\">":[321],"\u2286":[329],"<mml:msup>":[331],"<mml:mrow":[332],"class=\"MJX-TeXAtom-ORD\">":[333],"mathvariant=\"double-struck\">R</mml:mi>":[335],"<mml:mi>d</mml:mi>":[337,360],"</mml:msup>":[338],"encoding=\"application/x-tex\">\\Omega":[341],"\\subseteq":[342],"\\mathbb":[343],"{R}^d</mml:annotation>":[344],"alttext=\"d":[353],"2":[355],"3\">":[357],"<mml:mn>2</mml:mn>":[362],"<mml:mn>3</mml:mn>":[364],"encoding=\"application/x-tex\">d=2,3</mml:annotation>":[367],"By":[372],"using":[373],"regularization":[375],"technique,":[376],"we":[377],"propose":[378],"three":[379],"fully":[380],"discrete":[381],"Finite":[382],"Element":[383],"(FE)":[384],"approximations.":[385],"The":[386],"first":[387],"one":[388],"nonlinear":[391],"approximation":[392],"variables":[395]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
