{"id":"https://openalex.org/W3146594506","doi":"https://doi.org/10.3390/a14040113","title":"On a Robust and Efficient Numerical Scheme for the Simulation of Stationary 3-Component Systems with Non-Negative Species-Concentration with an Application to the Cu Deposition from a Cu-(\u03b2-alanine)-Electrolyte","display_name":"On a Robust and Efficient Numerical Scheme for the Simulation of Stationary 3-Component Systems with Non-Negative Species-Concentration with an Application to the Cu Deposition from a Cu-(\u03b2-alanine)-Electrolyte","publication_year":2021,"publication_date":"2021-03-30","ids":{"openalex":"https://openalex.org/W3146594506","doi":"https://doi.org/10.3390/a14040113","mag":"3146594506"},"language":"en","primary_location":{"id":"doi:10.3390/a14040113","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a14040113","pdf_url":"https://www.mdpi.com/1999-4893/14/4/113/pdf?version=1617938353","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/14/4/113/pdf?version=1617938353","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072572365","display_name":"Stephan Daniel Schwoebel","orcid":null},"institutions":[{"id":"https://openalex.org/I2610724","display_name":"Chemnitz University of Technology","ror":"https://ror.org/00a208s56","country_code":"DE","type":"education","lineage":["https://openalex.org/I2610724"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Stephan Daniel Schwoebel","raw_affiliation_strings":["Materials and Surface Engineering Group, Institute of Materials Science and Engineering, Chemnitz University of Technology, D-09107 Chemnitz, Germany"],"affiliations":[{"raw_affiliation_string":"Materials and Surface Engineering Group, Institute of Materials Science and Engineering, Chemnitz University of Technology, D-09107 Chemnitz, Germany","institution_ids":["https://openalex.org/I2610724"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073504983","display_name":"Thomas Mehner","orcid":"https://orcid.org/0000-0003-1554-170X"},"institutions":[{"id":"https://openalex.org/I2610724","display_name":"Chemnitz University of Technology","ror":"https://ror.org/00a208s56","country_code":"DE","type":"education","lineage":["https://openalex.org/I2610724"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Thomas Mehner","raw_affiliation_strings":["Materials and Surface Engineering Group, Institute of Materials Science and Engineering, Chemnitz University of Technology, D-09107 Chemnitz, Germany"],"affiliations":[{"raw_affiliation_string":"Materials and Surface Engineering Group, Institute of Materials Science and Engineering, Chemnitz University of Technology, D-09107 Chemnitz, Germany","institution_ids":["https://openalex.org/I2610724"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065591442","display_name":"Thomas Lampke","orcid":"https://orcid.org/0000-0002-2390-9159"},"institutions":[{"id":"https://openalex.org/I2610724","display_name":"Chemnitz University of Technology","ror":"https://ror.org/00a208s56","country_code":"DE","type":"education","lineage":["https://openalex.org/I2610724"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Thomas Lampke","raw_affiliation_strings":["Materials and Surface Engineering Group, Institute of Materials Science and Engineering, Chemnitz University of Technology, D-09107 Chemnitz, Germany"],"affiliations":[{"raw_affiliation_string":"Materials and Surface Engineering Group, Institute of Materials Science and Engineering, Chemnitz University of Technology, D-09107 Chemnitz, Germany","institution_ids":["https://openalex.org/I2610724"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5072572365"],"corresponding_institution_ids":["https://openalex.org/I2610724"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1354,"currency":"EUR","value_usd":1460},"fwci":0.1791,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.43814379,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"14","issue":"4","first_page":"113","last_page":"113"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.998199999332428,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.998199999332428,"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/T11188","display_name":"Coagulation and Flocculation Studies","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2312","display_name":"Water Science and Technology"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12274","display_name":"Electrostatics and Colloid Interactions","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/1606","display_name":"Physical and Theoretical Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-simulation","display_name":"Computer simulation","score":0.5834349393844604},{"id":"https://openalex.org/keywords/component","display_name":"Component (thermodynamics)","score":0.5226176381111145},{"id":"https://openalex.org/keywords/reaction\u2013diffusion-system","display_name":"Reaction\u2013diffusion system","score":0.5146394968032837},{"id":"https://openalex.org/keywords/electrolyte","display_name":"Electrolyte","score":0.5118717551231384},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5015959739685059},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.49557292461395264},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4860894978046417},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4611419141292572},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4402598738670349},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.43584758043289185},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.4345484673976898},{"id":"https://openalex.org/keywords/deposition","display_name":"Deposition (geology)","score":0.4193195700645447},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3386506140232086},{"id":"https://openalex.org/keywords/biological-system","display_name":"Biological system","score":0.3363798260688782},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3164241313934326},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.27251946926116943},{"id":"https://openalex.org/keywords/electrode","display_name":"Electrode","score":0.2168956696987152},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.21510669589042664},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.202866792678833},{"id":"https://openalex.org/keywords/physical-chemistry","display_name":"Physical chemistry","score":0.1976626217365265},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.15517932176589966},{"id":"https://openalex.org/keywords/simulation","display_name":"Simulation","score":0.15181347727775574},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13562175631523132}],"concepts":[{"id":"https://openalex.org/C500300565","wikidata":"https://www.wikidata.org/wiki/Q925667","display_name":"Computer simulation","level":2,"score":0.5834349393844604},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.5226176381111145},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.5146394968032837},{"id":"https://openalex.org/C68801617","wikidata":"https://www.wikidata.org/wiki/Q162908","display_name":"Electrolyte","level":3,"score":0.5118717551231384},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5015959739685059},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.49557292461395264},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4860894978046417},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4611419141292572},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4402598738670349},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.43584758043289185},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4345484673976898},{"id":"https://openalex.org/C64297162","wikidata":"https://www.wikidata.org/wiki/Q1987070","display_name":"Deposition (geology)","level":3,"score":0.4193195700645447},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3386506140232086},{"id":"https://openalex.org/C186060115","wikidata":"https://www.wikidata.org/wiki/Q30336093","display_name":"Biological system","level":1,"score":0.3363798260688782},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3164241313934326},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.27251946926116943},{"id":"https://openalex.org/C17525397","wikidata":"https://www.wikidata.org/wiki/Q176140","display_name":"Electrode","level":2,"score":0.2168956696987152},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.21510669589042664},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.202866792678833},{"id":"https://openalex.org/C147789679","wikidata":"https://www.wikidata.org/wiki/Q11372","display_name":"Physical chemistry","level":1,"score":0.1976626217365265},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.15517932176589966},{"id":"https://openalex.org/C44154836","wikidata":"https://www.wikidata.org/wiki/Q45045","display_name":"Simulation","level":1,"score":0.15181347727775574},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13562175631523132},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C2816523","wikidata":"https://www.wikidata.org/wiki/Q180184","display_name":"Sediment","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/a14040113","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a14040113","pdf_url":"https://www.mdpi.com/1999-4893/14/4/113/pdf?version=1617938353","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:38c13ffb312143d5b559be0fc3efa270","is_oa":true,"landing_page_url":"https://doaj.org/article/38c13ffb312143d5b559be0fc3efa270","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 14, Iss 4, p 113 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1999-4893/14/4/113/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/a14040113","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms; Volume 14; Issue 4; Pages: 113","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/a14040113","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a14040113","pdf_url":"https://www.mdpi.com/1999-4893/14/4/113/pdf?version=1617938353","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","score":0.6499999761581421,"display_name":"Life in Land"}],"awards":[{"id":"https://openalex.org/G2128445967","display_name":null,"funder_award_id":"ID 12-2021","funder_id":"https://openalex.org/F4320311034","funder_display_name":"Technische Universit\u00e4t Chemnitz"}],"funders":[{"id":"https://openalex.org/F4320311034","display_name":"Technische Universit\u00e4t Chemnitz","ror":"https://ror.org/00a208s56"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3146594506.pdf","grobid_xml":"https://content.openalex.org/works/W3146594506.grobid-xml"},"referenced_works_count":56,"referenced_works":["https://openalex.org/W3347125","https://openalex.org/W119711759","https://openalex.org/W169396209","https://openalex.org/W189598787","https://openalex.org/W592911714","https://openalex.org/W601797399","https://openalex.org/W651774878","https://openalex.org/W1513782764","https://openalex.org/W1555557982","https://openalex.org/W1581406479","https://openalex.org/W1876188899","https://openalex.org/W1978687734","https://openalex.org/W1984848663","https://openalex.org/W1987700684","https://openalex.org/W1989157562","https://openalex.org/W2026365342","https://openalex.org/W2028811441","https://openalex.org/W2033956894","https://openalex.org/W2039924562","https://openalex.org/W2041684917","https://openalex.org/W2054135182","https://openalex.org/W2067023906","https://openalex.org/W2068343977","https://openalex.org/W2068537445","https://openalex.org/W2071928229","https://openalex.org/W2074987839","https://openalex.org/W2092037996","https://openalex.org/W2164410804","https://openalex.org/W2167657634","https://openalex.org/W2316645408","https://openalex.org/W2476437723","https://openalex.org/W2493422191","https://openalex.org/W2526264695","https://openalex.org/W2564337945","https://openalex.org/W2616717838","https://openalex.org/W2765080741","https://openalex.org/W2767740401","https://openalex.org/W2786622712","https://openalex.org/W2909105280","https://openalex.org/W2942970966","https://openalex.org/W2950880783","https://openalex.org/W2985272081","https://openalex.org/W3016893089","https://openalex.org/W3098828867","https://openalex.org/W3139348098","https://openalex.org/W4236384742","https://openalex.org/W4237715993","https://openalex.org/W4243140258","https://openalex.org/W4245588718","https://openalex.org/W4248049412","https://openalex.org/W4248081355","https://openalex.org/W4255355970","https://openalex.org/W4255859732","https://openalex.org/W4256277922","https://openalex.org/W4290935769","https://openalex.org/W6982904292"],"related_works":["https://openalex.org/W2393651404","https://openalex.org/W2124062602","https://openalex.org/W4226416379","https://openalex.org/W2374930247","https://openalex.org/W2374309527","https://openalex.org/W2548222822","https://openalex.org/W2049181797","https://openalex.org/W1974862832","https://openalex.org/W2094510435","https://openalex.org/W3131359455"],"abstract_inverted_index":{"Three-component":[0],"systems":[1,34],"of":[2,14,32,65,77,89],"diffusion\u2013reaction":[3,110],"equations":[4],"play":[5],"a":[6,84,87,103],"central":[7],"role":[8],"in":[9,17,29,42,63,116],"the":[10,30,43,78,119],"modelling":[11],"and":[12,45,68,96,105],"simulation":[13,31],"chemical":[15],"processes":[16],"engineering,":[18],"electro-chemistry,":[19],"physical":[20],"chemistry,":[21],"biology,":[22],"population":[23],"dynamics,":[24],"etc.":[25],"A":[26],"major":[27],"question":[28],"three-component":[33],"is":[35,99,122],"how":[36,46],"to":[37,47,54,60,101,108,134],"guarantee":[38],"non-negative":[39,56,113],"species":[40,57],"distributions":[41,58],"model":[44],"calculate":[48],"them":[49],"effectively.":[50],"Current":[51],"numerical":[52,127],"methods":[53],"enforce":[55],"tend":[59],"be":[61],"cost-intensive":[62],"terms":[64],"computation":[66],"time":[67],"they":[69],"are":[70,141],"not":[71,123],"robust":[72,104],"for":[73],"big":[74],"rate":[75],"constants":[76],"considered":[79],"reaction.":[80],"In":[81],"this":[82,117],"article,":[83],"method,":[85],"as":[86,129,131],"combination":[88],"homotopy":[90],"methods,":[91,95],"modern":[92],"augmented":[93],"Lagrangian":[94],"adaptive":[97],"FEMs":[98],"outlined":[100],"obtain":[102],"efficient":[106],"method":[107],"simulate":[109],"models":[111],"with":[112],"concentrations.":[114],"Although":[115],"paper":[118],"convergence":[120],"analysis":[121],"described":[124],"rigorously,":[125],"multiple":[126],"examples":[128],"well":[130],"an":[132,137],"application":[133],"elctro-deposition":[135],"from":[136],"aqueous":[138],"Cu2+-(\u03b2-alanine)":[139],"electrolyte":[140],"presented.":[142]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2021-04-13T00:00:00"}
