{"id":"https://openalex.org/W1968167524","doi":"https://doi.org/10.3390/axioms3020280","title":"A Comparative Study of Several Classical, Discrete Differential and Isogeometric Methods for Solving Poisson\u2019s Equation on the Disk","display_name":"A Comparative Study of Several Classical, Discrete Differential and Isogeometric Methods for Solving Poisson\u2019s Equation on the Disk","publication_year":2014,"publication_date":"2014-06-11","ids":{"openalex":"https://openalex.org/W1968167524","doi":"https://doi.org/10.3390/axioms3020280","mag":"1968167524"},"language":"en","primary_location":{"id":"doi:10.3390/axioms3020280","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms3020280","pdf_url":"https://www.mdpi.com/2075-1680/3/2/280/pdf?version=1402496786","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/3/2/280/pdf?version=1402496786","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038209803","display_name":"Thien Nguyen","orcid":"https://orcid.org/0000-0002-5319-1213"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Thien Nguyen","raw_affiliation_strings":["Department of Computer and Information Science and Engineering, University of Florida, Gainesville, FL 32611, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer and Information Science and Engineering, University of Florida, Gainesville, FL 32611, USA","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068895473","display_name":"Ke\u00e7stutis Kar\u010diauskas","orcid":null},"institutions":[{"id":"https://openalex.org/I173212132","display_name":"Vilnius University","ror":"https://ror.org/03nadee84","country_code":"LT","type":"education","lineage":["https://openalex.org/I173212132"]}],"countries":["LT"],"is_corresponding":false,"raw_author_name":"Ke\u00e7stutis Kar\u010diauskas","raw_affiliation_strings":["Department of Mathematics, Vilnius University, LT-01513 Vilnius, Lithuania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Vilnius University, LT-01513 Vilnius, Lithuania","institution_ids":["https://openalex.org/I173212132"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027686327","display_name":"J\u00f6rg Peters","orcid":"https://orcid.org/0000-0002-2499-1529"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"J\u00f6rg Peters","raw_affiliation_strings":["Department of Computer and Information Science and Engineering, University of Florida, Gainesville, FL 32611, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer and Information Science and Engineering, University of Florida, Gainesville, FL 32611, USA","institution_ids":["https://openalex.org/I33213144"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5027686327"],"corresponding_institution_ids":["https://openalex.org/I33213144"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":14.3467,"has_fulltext":false,"cited_by_count":97,"citation_normalized_percentile":{"value":0.99493231,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"3","issue":"2","first_page":"280","last_page":"299"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9998999834060669,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9998999834060669,"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/isogeometric-analysis","display_name":"Isogeometric analysis","score":0.8982105255126953},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6766954064369202},{"id":"https://openalex.org/keywords/poissons-equation","display_name":"Poisson's equation","score":0.6115534901618958},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.6035435199737549},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5150256156921387},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.5116284489631653},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5048657059669495},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4654230773448944},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.36246374249458313},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35611093044281006},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.20327472686767578}],"concepts":[{"id":"https://openalex.org/C2780737243","wikidata":"https://www.wikidata.org/wiki/Q17082433","display_name":"Isogeometric analysis","level":3,"score":0.8982105255126953},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6766954064369202},{"id":"https://openalex.org/C96716743","wikidata":"https://www.wikidata.org/wiki/Q827688","display_name":"Poisson's equation","level":2,"score":0.6115534901618958},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.6035435199737549},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5150256156921387},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.5116284489631653},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5048657059669495},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4654230773448944},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.36246374249458313},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35611093044281006},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20327472686767578},{"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms3020280","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms3020280","pdf_url":"https://www.mdpi.com/2075-1680/3/2/280/pdf?version=1402496786","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:4a0b5d35118c49759e04d3accdd57b1d","is_oa":true,"landing_page_url":"https://doaj.org/article/4a0b5d35118c49759e04d3accdd57b1d","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 3, Iss 2, Pp 280-299 (2014)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/3/2/280/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms3020280","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":"Axioms; Volume 3; Issue 2; Pages: 280-299","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms3020280","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms3020280","pdf_url":"https://www.mdpi.com/2075-1680/3/2/280/pdf?version=1402496786","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W43399846","https://openalex.org/W137649219","https://openalex.org/W592368443","https://openalex.org/W603006721","https://openalex.org/W629836974","https://openalex.org/W1570866526","https://openalex.org/W1587541211","https://openalex.org/W1763606621","https://openalex.org/W1974956622","https://openalex.org/W1980220299","https://openalex.org/W1989151181","https://openalex.org/W2000214666","https://openalex.org/W2000425991","https://openalex.org/W2003515735","https://openalex.org/W2040398764","https://openalex.org/W2041797304","https://openalex.org/W2054361378","https://openalex.org/W2056816721","https://openalex.org/W2060365416","https://openalex.org/W2068967700","https://openalex.org/W2074623661","https://openalex.org/W2081893716","https://openalex.org/W2090236665","https://openalex.org/W2093452368","https://openalex.org/W2120103450","https://openalex.org/W2131480283","https://openalex.org/W2153399947","https://openalex.org/W2162870748","https://openalex.org/W2229156033","https://openalex.org/W2249925049","https://openalex.org/W2293994889","https://openalex.org/W2320271346","https://openalex.org/W2406166363","https://openalex.org/W2950410840","https://openalex.org/W2963329337","https://openalex.org/W3125695748","https://openalex.org/W3138586438","https://openalex.org/W4239919514","https://openalex.org/W4253143386","https://openalex.org/W4293102147","https://openalex.org/W6635325155","https://openalex.org/W6713854818","https://openalex.org/W6921659658"],"related_works":["https://openalex.org/W1940709639","https://openalex.org/W1924025565","https://openalex.org/W3025313650","https://openalex.org/W2352095914","https://openalex.org/W2989766329","https://openalex.org/W2129372062","https://openalex.org/W2981315515","https://openalex.org/W4297362898","https://openalex.org/W2624186518","https://openalex.org/W2110186881"],"abstract_inverted_index":{"This":[0],"paper":[1],"outlines":[2],"and":[3,33],"qualitatively":[4],"compares":[5],"the":[6,17,52,77,100],"implementations":[7],"of":[8],"seven":[9,60],"different":[10],"methods":[11,20,61,72],"for":[12,45],"solving":[13],"Poisson\u2019s":[14],"equation":[15],"on":[16,49,95],"disk.":[18],"The":[19,37,59],"include":[21,62],"two":[22,63],"classical":[23],"finite":[24],"elements,":[25,51],"a":[26,96,103],"cotan":[27],"formula-based":[28],"discrete":[29],"differential":[30],"geometry":[31],"approach":[32],"four":[34],"isogeometric":[35,46,68],"constructions.":[36],"comparison":[38],"reveals":[39],"numerical":[40],"convergence":[41,75],"rates":[42],"and,":[43],"particularly":[44],"constructions":[47],"based":[48,94],"Catmull\u2013Clark":[50],"need":[53],"to":[54,67],"carefully":[55],"choose":[56],"quadrature":[57],"formulas.":[58],"that":[64],"are":[65,83],"new":[66,71],"analysis.":[69],"Both":[70],"yield":[73],"O(h3)":[74],"in":[76],"L2":[78],"norm,":[79],"also":[80],"when":[81],"points":[82],"included":[84],"where":[85],"n":[86],"6\u2260":[87],"4":[88],"pieces":[89],"meet.":[90],"One":[91],"construction":[92],"is":[93,102],"polar,":[97],"singular":[98],"parameterization;":[99],"other":[101],"G1":[104],"tensor-product":[105],"construction.":[106]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":14},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":21},{"year":2016,"cited_by_count":14},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2016-06-24T00:00:00"}
