{"id":"https://openalex.org/W4414575956","doi":"https://doi.org/10.1137/25m1765857","title":"A Structure-Preserving and Thermodynamically Compatible Cell-Centered Lagrangian Finite Volume Scheme for Continuum Mechanics","display_name":"A Structure-Preserving and Thermodynamically Compatible Cell-Centered Lagrangian Finite Volume Scheme for Continuum Mechanics","publication_year":2026,"publication_date":"2026-05-22","ids":{"openalex":"https://openalex.org/W4414575956","doi":"https://doi.org/10.1137/25m1765857"},"language":"en","primary_location":{"id":"doi:10.1137/25m1765857","is_oa":false,"landing_page_url":"https://doi.org/10.1137/25m1765857","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2506.03081","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062552716","display_name":"Walter Boscheri","orcid":"https://orcid.org/0000-0002-1467-1679"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I201324441","display_name":"University of Ferrara","ror":"https://ror.org/041zkgm14","country_code":"IT","type":"education","lineage":["https://openalex.org/I201324441"]},{"id":"https://openalex.org/I4210144844","display_name":"Laboratoire d\u2019Analyse et de Math\u00e9matiques Appliqu\u00e9es","ror":"https://ror.org/0581g8849","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I197681013","https://openalex.org/I4210141950","https://openalex.org/I4210144844","https://openalex.org/I4210154111"]},{"id":"https://openalex.org/I4210155549","display_name":"Laboratoire de Math\u00e9matiques Blaise Pascal","ror":"https://ror.org/05sd5r855","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I198244214","https://openalex.org/I4210141950","https://openalex.org/I4210155549"]},{"id":"https://openalex.org/I70900168","display_name":"Universit\u00e9 Savoie Mont Blanc","ror":"https://ror.org/04gqg1a07","country_code":"FR","type":"education","lineage":["https://openalex.org/I70900168"]}],"countries":["FR","IT"],"is_corresponding":false,"raw_author_name":"Walter Boscheri","raw_affiliation_strings":["Laboratoire de Math\u00e9matiques UMR 5127 CNRS, Universit\u00e9 Savoie Mont Blanc, 73376 Le Bourget du Lac, France, and Department of Mathematics and Computer Science, University of Ferrara, 44121, Ferrara, Italy","LAMA - Laboratoire de Math\u00e9matiques (Universit\u00e9 Savoie Mont Blanc, Campus Scientifique, B\u00e2timent Le Chablais  73376 Le Bourget du Lac, France - France)"],"raw_orcid":"https://orcid.org/0000-0002-1467-1679","affiliations":[{"raw_affiliation_string":"Laboratoire de Math\u00e9matiques UMR 5127 CNRS, Universit\u00e9 Savoie Mont Blanc, 73376 Le Bourget du Lac, France, and Department of Mathematics and Computer Science, University of Ferrara, 44121, Ferrara, Italy","institution_ids":["https://openalex.org/I70900168","https://openalex.org/I201324441","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"LAMA - Laboratoire de Math\u00e9matiques (Universit\u00e9 Savoie Mont Blanc, Campus Scientifique, B\u00e2timent Le Chablais  73376 Le Bourget du Lac, France - France)","institution_ids":["https://openalex.org/I70900168","https://openalex.org/I4210144844","https://openalex.org/I4210155549"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051559583","display_name":"Michael Dumbser","orcid":"https://orcid.org/0000-0002-8201-8372"},"institutions":[{"id":"https://openalex.org/I193223587","display_name":"University of Trento","ror":"https://ror.org/05trd4x28","country_code":"IT","type":"education","lineage":["https://openalex.org/I193223587"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Michael Dumbser","raw_affiliation_strings":["Department of Civil, Environmental and Mechanical Engineering, University of Trento, 38123 Trento, Italy","UNITN - Universit\u00e0 degli Studi di Trento =  University of Trento (via Calepina, 14 - I-38122 Trento - Italy)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Civil, Environmental and Mechanical Engineering, University of Trento, 38123 Trento, Italy","institution_ids":["https://openalex.org/I193223587"]},{"raw_affiliation_string":"UNITN - Universit\u00e0 degli Studi di Trento =  University of Trento (via Calepina, 14 - I-38122 Trento - Italy)","institution_ids":["https://openalex.org/I193223587"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079701082","display_name":"Rapha\u00ebl Loub\u00e8re","orcid":"https://orcid.org/0000-0002-1249-1578"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I15057530","display_name":"Universit\u00e9 de Bordeaux","ror":"https://ror.org/057qpr032","country_code":"FR","type":"education","lineage":["https://openalex.org/I15057530"]},{"id":"https://openalex.org/I4210166017","display_name":"Institut de Math\u00e9matiques de Bordeaux","ror":"https://ror.org/05m3r1b84","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I15057530","https://openalex.org/I4210141950","https://openalex.org/I4210160189","https://openalex.org/I4210166017"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Rapha\u00ebl Loub\u00e8re","raw_affiliation_strings":["Institut de Math\u00e9matiques de Bordeaux (IMB), UMR, 5251 Universit\u00e9 de Bordeaux, CNRS, Bordeaux, INP, Talence, F-33400, France","IMB - Institut de Math\u00e9matiques de Bordeaux (351 cours de la Lib\u00e9ration 33405 TALENCE CEDEX - France)"],"raw_orcid":"https://orcid.org/0000-0002-1249-1578","affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matiques de Bordeaux (IMB), UMR, 5251 Universit\u00e9 de Bordeaux, CNRS, Bordeaux, INP, Talence, F-33400, France","institution_ids":["https://openalex.org/I4210166017","https://openalex.org/I15057530","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"IMB - Institut de Math\u00e9matiques de Bordeaux (351 cours de la Lib\u00e9ration 33405 TALENCE CEDEX - France)","institution_ids":["https://openalex.org/I4210166017"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009494555","display_name":"Pierre\u2010Henri Maire","orcid":"https://orcid.org/0000-0002-4180-8220"},"institutions":[{"id":"https://openalex.org/I129235615","display_name":"CEA CESTA","ror":"https://ror.org/026ma2c10","country_code":"FR","type":"government","lineage":["https://openalex.org/I129235615","https://openalex.org/I4210101455"]},{"id":"https://openalex.org/I2738703131","display_name":"Commissariat \u00e0 l'\u00c9nergie Atomique et aux \u00c9nergies Alternatives","ror":"https://ror.org/00jjx8s55","country_code":"FR","type":"government","lineage":["https://openalex.org/I2738703131"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Pierre-Henri Maire","raw_affiliation_strings":["CEA CESTA, 33116 Le Barp, France","CESTA - Centre d'\u00e9tudes scientifiques et techniques d'Aquitaine (CESTA-CEA) (BP 2 33114 Le Barp - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CEA CESTA, 33116 Le Barp, France","institution_ids":["https://openalex.org/I2738703131","https://openalex.org/I129235615"]},{"raw_affiliation_string":"CESTA - Centre d'\u00e9tudes scientifiques et techniques d'Aquitaine (CESTA-CEA) (BP 2 33114 Le Barp - France)","institution_ids":["https://openalex.org/I2738703131","https://openalex.org/I129235615"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"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":0.00676211,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"64","issue":"3","first_page":"685","last_page":"707"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","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"}},"topics":[{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","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"}},{"id":"https://openalex.org/T11366","display_name":"Elasticity and Material Modeling","score":0.9929999709129333,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9922000169754028,"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":0.722100019454956},{"id":"https://openalex.org/keywords/conservation-law","display_name":"Conservation law","score":0.6694999933242798},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.555899977684021},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5313000082969666},{"id":"https://openalex.org/keywords/second-law-of-thermodynamics","display_name":"Second law of thermodynamics","score":0.4684999883174896},{"id":"https://openalex.org/keywords/compatibility","display_name":"Compatibility (geochemistry)","score":0.44830000400543213},{"id":"https://openalex.org/keywords/finite-volume-method","display_name":"Finite volume method","score":0.4214000105857849},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.3822000026702881},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.3560999929904938}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7283999919891357},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.722100019454956},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.6694999933242798},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.555899977684021},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5313000082969666},{"id":"https://openalex.org/C119820323","wikidata":"https://www.wikidata.org/wiki/Q177045","display_name":"Second law of thermodynamics","level":2,"score":0.4684999883174896},{"id":"https://openalex.org/C2778648169","wikidata":"https://www.wikidata.org/wiki/Q967768","display_name":"Compatibility (geochemistry)","level":2,"score":0.44830000400543213},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.4214000105857849},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4212999939918518},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41449999809265137},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3822000026702881},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.3560999929904938},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.35269999504089355},{"id":"https://openalex.org/C84035572","wikidata":"https://www.wikidata.org/wiki/Q193463","display_name":"Continuum mechanics","level":2,"score":0.33820000290870667},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.31220000982284546},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.30959999561309814},{"id":"https://openalex.org/C520301825","wikidata":"https://www.wikidata.org/wiki/Q380170","display_name":"Energy conservation","level":2,"score":0.3089999854564667},{"id":"https://openalex.org/C96314035","wikidata":"https://www.wikidata.org/wiki/Q5282062","display_name":"Discrete system","level":2,"score":0.2996000051498413},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.2919999957084656},{"id":"https://openalex.org/C52957995","wikidata":"https://www.wikidata.org/wiki/Q11382","display_name":"Conservation of energy","level":2,"score":0.2897999882698059},{"id":"https://openalex.org/C29660869","wikidata":"https://www.wikidata.org/wiki/Q5282615","display_name":"Displacement field","level":3,"score":0.2842999994754791},{"id":"https://openalex.org/C70836080","wikidata":"https://www.wikidata.org/wiki/Q837940","display_name":"Impulse (physics)","level":2,"score":0.28040000796318054},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.25540000200271606},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.2540000081062317},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.25110000371932983},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.250900000333786}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/25m1765857","is_oa":false,"landing_page_url":"https://doi.org/10.1137/25m1765857","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:arXiv.org:2506.03081","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2506.03081","pdf_url":"https://arxiv.org/pdf/2506.03081","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":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-05176480v1","is_oa":true,"landing_page_url":"https://hal.science/hal-05176480","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"2025","raw_type":"Preprints, Working Papers, ..."},{"id":"doi:10.48550/arxiv.2506.03081","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2506.03081","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":"pmh:oai:arXiv.org:2506.03081","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2506.03081","pdf_url":"https://arxiv.org/pdf/2506.03081","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":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2739175211","display_name":null,"funder_award_id":"L. 232/2016","funder_id":"https://openalex.org/F4320322275","funder_display_name":"Universit\u00e0 degli Studi di Trento"},{"id":"https://openalex.org/G8919731619","display_name":null,"funder_award_id":"ERC-ADG-2021-101052956-BEYOND","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"}],"funders":[{"id":"https://openalex.org/F4320322275","display_name":"Universit\u00e0 degli Studi di Trento","ror":"https://ror.org/05trd4x28"},{"id":"https://openalex.org/F4320325935","display_name":"Fondazione Cassa Di Risparmio Di Trento E Rovereto","ror":"https://ror.org/02pgnjz11"},{"id":"https://openalex.org/F4320338335","display_name":"H2020 European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4414575956.pdf","grobid_xml":"https://content.openalex.org/works/W4414575956.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0],"this":[1,109],"work":[2,110],"we":[3,224],"present":[4],"a":[5,68,102,116,238],"novel":[6],"structure-preserving":[7],"scheme":[8,125],"for":[9,31],"the":[10,13,32,41,50,56,60,63,72,81,84,90,93,96,132,137,142,148,161,175,178,181,188,192,197,202,229,249],"discretization":[11,246],"of":[12,17,37,46,52,59,83,92,108,136,151,164,180,187,191,196,204,240,247],"Godunov-Peshkov-Romenski":[14],"(GPR)":[15],"model":[16,25],"continuum":[18,61],"mechanics":[19],"written":[20],"in":[21,49,201,221],"Lagrangian":[22,122],"form.":[23],"This":[24],"admits":[26],"an":[27,241],"extra":[28],"conservation":[29,236],"law":[30,150,163],"total":[33,155,234],"energy":[34,156,235],"(first":[35],"principle":[36,45],"thermodynamics)":[38],"and":[39,62,114,177,195,243],"satisfies":[40,131],"entropy":[42,168,230],"inequality":[43],"(second":[44],"thermodynamics).":[47],"Furthermore,":[48],"absence":[51,203],"algebraic":[53,104,205],"source":[54,206],"terms,":[55],"distortion":[57,85,182,193],"field":[58,86,194],"specific":[64,198],"thermal":[65,199],"impulse":[66,200],"satisfy":[67],"curl-free":[69,189],"condition,":[70],"provided":[71],"initial":[73],"data":[74],"are":[75],"curl-free.":[76],"Last":[77],"but":[78],"not":[79],"least,":[80],"determinant":[82,179],"is":[87,98,111,212],"related":[88],"to":[89,112,214,226],"density":[91,176],"medium,":[94],"i.e.":[95,153,166],"system":[97],"also":[99],"endowed":[100],"with":[101,147,160],"nonlinear":[103],"constraint.":[105],"The":[106],"objective":[107],"construct":[113],"analyze":[115],"new":[117],"semi-discrete":[118],"thermodynamically":[119,244],"compatible":[120,245],"cell-centered":[121],"finite":[123],"volume":[124],"on":[126],"moving":[127],"unstructured":[128],"meshes":[129],"that":[130,210],"following":[133],"structural":[134],"properties":[135,218],"governing":[138],"PDE":[139],"exactly":[140],"at":[141],"discrete":[143,154,167,172],"level:":[144],"i)":[145],"compatibility":[146,159,173],"first":[149],"thermodynamics,":[152,165],"conservation;":[157],"ii)":[158],"second":[162],"inequality;":[169],"iii)":[170],"exact":[171,185],"between":[174],"field;":[183],"iv)":[184],"preservation":[186],"property":[190],"terms.":[207],"We":[208],"show":[209],"it":[211],"possible":[213],"achieve":[215],"all":[216,248],"above":[217],"simultaneously.":[219],"Unlike":[220],"existing":[222],"schemes,":[223],"choose":[225],"directly":[227],"discretize":[228],"inequality,":[231],"hence":[232],"obtaining":[233],"as":[237],"consequence":[239],"appropriate":[242],"other":[250],"equations.":[251]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}