{"id":"https://openalex.org/W4402093168","doi":"https://doi.org/10.1007/s11075-024-01919-4","title":"VEMcomp: a Virtual Elements MATLAB package for bulk-surface PDEs in 2D and 3D","display_name":"VEMcomp: a Virtual Elements MATLAB package for bulk-surface PDEs in 2D and 3D","publication_year":2024,"publication_date":"2024-08-31","ids":{"openalex":"https://openalex.org/W4402093168","doi":"https://doi.org/10.1007/s11075-024-01919-4","pmid":"https://pubmed.ncbi.nlm.nih.gov/40538771"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-024-01919-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-024-01919-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-024-01919-4.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11075-024-01919-4.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020028375","display_name":"Massimo Frittelli","orcid":"https://orcid.org/0000-0002-1774-9320"},"institutions":[{"id":"https://openalex.org/I142910587","display_name":"University of Salento","ror":"https://ror.org/03fc1k060","country_code":"IT","type":"education","lineage":["https://openalex.org/I142910587"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Massimo Frittelli","raw_affiliation_strings":["Department of Mathematics and Physics \"E. De Giorgi\", Via per Arnesano, University of Salento, 73100 Lecce, Italy","Department of Mathematics and Physics \"E. De Giorgi\", Via per Arnesano, University of Salento, 73100, Lecce, Italy"],"raw_orcid":"https://orcid.org/0000-0002-1774-9320","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Physics \"E. De Giorgi\", Via per Arnesano, University of Salento, 73100 Lecce, Italy","institution_ids":["https://openalex.org/I142910587"]},{"raw_affiliation_string":"Department of Mathematics and Physics \"E. De Giorgi\", Via per Arnesano, University of Salento, 73100, Lecce, Italy","institution_ids":["https://openalex.org/I142910587"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075584405","display_name":"Anotida Madzvamuse","orcid":"https://orcid.org/0000-0002-9511-8903"},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]},{"id":"https://openalex.org/I153455119","display_name":"University of Zimbabwe","ror":"https://ror.org/04ze6rb18","country_code":"ZW","type":"education","lineage":["https://openalex.org/I153455119"]},{"id":"https://openalex.org/I24027795","display_name":"University of Johannesburg","ror":"https://ror.org/04z6c2n17","country_code":"ZA","type":"education","lineage":["https://openalex.org/I24027795"]},{"id":"https://openalex.org/I69552723","display_name":"University of Pretoria","ror":"https://ror.org/00g0p6g84","country_code":"ZA","type":"education","lineage":["https://openalex.org/I69552723"]}],"countries":["CA","ZA","ZW"],"is_corresponding":false,"raw_author_name":"Anotida Madzvamuse","raw_affiliation_strings":["Department of Mathematics and Applied Mathematics, University of Johannesburg, PO Box 524, Auckland Park, 2006 South Africa","Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, 0132 South Africa","Department of Mathematics and Computational Science, Faculty of Science, University of Zimbabwe, Mount Pleasant, Harare, Zimbabwe","Mathematics Department, The University of British Columbia, Vancouver, British Columbia Canada","Mathematics Department, The University of British Columbia, Vancouver, British Columbia, Canada","Department of Mathematics and Applied Mathematics, University of Johannesburg, PO Box 524, Auckland Park, 2006, South Africa","Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, 0132, South Africa"],"raw_orcid":"https://orcid.org/0000-0002-9511-8903","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Applied Mathematics, University of Johannesburg, PO Box 524, Auckland Park, 2006 South Africa","institution_ids":["https://openalex.org/I24027795"]},{"raw_affiliation_string":"Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, 0132 South Africa","institution_ids":["https://openalex.org/I69552723"]},{"raw_affiliation_string":"Department of Mathematics and Computational Science, Faculty of Science, University of Zimbabwe, Mount Pleasant, Harare, Zimbabwe","institution_ids":["https://openalex.org/I153455119"]},{"raw_affiliation_string":"Mathematics Department, The University of British Columbia, Vancouver, British Columbia Canada","institution_ids":["https://openalex.org/I141945490"]},{"raw_affiliation_string":"Mathematics Department, The University of British Columbia, Vancouver, British Columbia, Canada","institution_ids":["https://openalex.org/I141945490"]},{"raw_affiliation_string":"Department of Mathematics and Applied Mathematics, University of Johannesburg, PO Box 524, Auckland Park, 2006, South Africa","institution_ids":["https://openalex.org/I24027795"]},{"raw_affiliation_string":"Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, 0132, South Africa","institution_ids":["https://openalex.org/I69552723"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009350643","display_name":"Ivonne Sgura","orcid":"https://orcid.org/0000-0001-9207-5832"},"institutions":[{"id":"https://openalex.org/I142910587","display_name":"University of Salento","ror":"https://ror.org/03fc1k060","country_code":"IT","type":"education","lineage":["https://openalex.org/I142910587"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Ivonne Sgura","raw_affiliation_strings":["Department of Mathematics and Physics \"E. De Giorgi\", Via per Arnesano, University of Salento, 73100 Lecce, Italy","Department of Mathematics and Physics \"E. De Giorgi\", Via per Arnesano, University of Salento, 73100, Lecce, Italy"],"raw_orcid":"https://orcid.org/0000-0001-9207-5832","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Physics \"E. De Giorgi\", Via per Arnesano, University of Salento, 73100 Lecce, Italy","institution_ids":["https://openalex.org/I142910587"]},{"raw_affiliation_string":"Department of Mathematics and Physics \"E. De Giorgi\", Via per Arnesano, University of Salento, 73100, Lecce, Italy","institution_ids":["https://openalex.org/I142910587"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5020028375"],"corresponding_institution_ids":["https://openalex.org/I142910587"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.9056,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.69175824,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":97},"biblio":{"volume":"99","issue":"3","first_page":"1393","last_page":"1428"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9994999766349792,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9994999766349792,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9904999732971191,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.989300012588501,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.6733901500701904},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.6122734546661377},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5947466492652893},{"id":"https://openalex.org/keywords/matlab","display_name":"MATLAB","score":0.5858860015869141},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5176037549972534},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5173410773277283},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.47917166352272034},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.4489178955554962},{"id":"https://openalex.org/keywords/mesh-generation","display_name":"Mesh generation","score":0.4349370300769806},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3924291431903839},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.3813154399394989},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3708992004394531},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2110445201396942},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1519017219543457},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.12761420011520386},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.09653130173683167}],"concepts":[{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.6733901500701904},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6122734546661377},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5947466492652893},{"id":"https://openalex.org/C2780365114","wikidata":"https://www.wikidata.org/wiki/Q169478","display_name":"MATLAB","level":2,"score":0.5858860015869141},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5176037549972534},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5173410773277283},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47917166352272034},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.4489178955554962},{"id":"https://openalex.org/C181145010","wikidata":"https://www.wikidata.org/wiki/Q4418033","display_name":"Mesh generation","level":3,"score":0.4349370300769806},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3924291431903839},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.3813154399394989},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3708992004394531},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2110445201396942},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1519017219543457},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.12761420011520386},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.09653130173683167},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s11075-024-01919-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-024-01919-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-024-01919-4.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},{"id":"pmid:40538771","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/40538771","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical algorithms","raw_type":null},{"id":"pmh:oai:repository.up.ac.za:2263/101275","is_oa":true,"landing_page_url":"http://hdl.handle.net/2263/101275","pdf_url":"https://repository.up.ac.za/bitstreams/c96fb003-54a0-4f41-b009-4d1b98952bd4/download","source":{"id":"https://openalex.org/S4306401870","display_name":"UpSpace Institutional Repository (University of Pretoria)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I69552723","host_organization_name":"University of Pretoria","host_organization_lineage":["https://openalex.org/I69552723"],"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":null,"raw_type":"Article"},{"id":"pmh:oai:figshare.com:article/28983437","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/VEMcomp_a_Virtual_Elements_MATLAB_package_for_bulk-surface_PDEs_in_2D_and_3D/28983437","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"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":null,"raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:12174232","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/12174232","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Numer Algorithms","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1007/s11075-024-01919-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-024-01919-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-024-01919-4.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1032224978","display_name":null,"funder_award_id":"PRIN project code P20228C2PP_001, CUP F53D23010020001","funder_id":"https://openalex.org/F4320331528","funder_display_name":"Ministero dell'Universit\u00e0 e della Ricerca"},{"id":"https://openalex.org/G1761237547","display_name":null,"funder_award_id":"F53D23010020001","funder_id":"https://openalex.org/F4320321873","funder_display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca"},{"id":"https://openalex.org/G2876861147","display_name":null,"funder_award_id":"CUP_E53C22001930001","funder_id":"https://openalex.org/F4320321873","funder_display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca"},{"id":"https://openalex.org/G3708853832","display_name":null,"funder_award_id":"PRIN2022","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G3918974238","display_name":null,"funder_award_id":"CUP_E53C22001930001","funder_id":"https://openalex.org/F4320334079","funder_display_name":"Gruppo Nazionale per il Calcolo Scientifico"},{"id":"https://openalex.org/G4954013139","display_name":null,"funder_award_id":"PRIN2022","funder_id":"https://openalex.org/F4320321873","funder_display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca"},{"id":"https://openalex.org/G5057163746","display_name":null,"funder_award_id":"EPSRC: EP/J016780/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5148775208","display_name":null,"funder_award_id":"GNCS project \"Metodi avanzati per la risoluzione di PDEs su griglie strutturate, e non\" CUP_E53C22001930001","funder_id":"https://openalex.org/F4320311030","funder_display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\""},{"id":"https://openalex.org/G5171083709","display_name":null,"funder_award_id":"CRC-2022-00147","funder_id":"https://openalex.org/F4320320994","funder_display_name":"Canada Research Chairs"},{"id":"https://openalex.org/G5469963565","display_name":null,"funder_award_id":"REFIN project, protocol code 901D2CAA, project no. UNISAL026","funder_id":"https://openalex.org/F4320326082","funder_display_name":"Regione Puglia"},{"id":"https://openalex.org/G5567526078","display_name":null,"funder_award_id":"UNISAL026","funder_id":"https://openalex.org/F4320326082","funder_display_name":"Regione Puglia"},{"id":"https://openalex.org/G570629271","display_name":null,"funder_award_id":"EP/J016780/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6104029035","display_name":"Modelling, analysis and simulation of spatial patterning on evolving surfaces","funder_award_id":"EP/J016780/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6559942121","display_name":null,"funder_award_id":"CUP_E53C22001930001","funder_id":"https://openalex.org/F4320311030","funder_display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\""},{"id":"https://openalex.org/G8080639462","display_name":null,"funder_award_id":"901D2CAA","funder_id":"https://openalex.org/F4320326082","funder_display_name":"Regione Puglia"}],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320314731","display_name":"UK Research and Innovation","ror":"https://ror.org/001aqnf71"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320994","display_name":"Canada Research Chairs","ror":"https://ror.org/0517h6h17"},{"id":"https://openalex.org/F4320321873","display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","ror":"https://ror.org/0166hxq48"},{"id":"https://openalex.org/F4320326082","display_name":"Regione Puglia","ror":"https://ror.org/039k11f95"},{"id":"https://openalex.org/F4320331528","display_name":"Ministero dell'Universit\u00e0 e della Ricerca","ror":null},{"id":"https://openalex.org/F4320334079","display_name":"Gruppo Nazionale per il Calcolo Scientifico","ror":null},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320335271","display_name":"British Columbia Knowledge Development Fund","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4402093168.pdf"},"referenced_works_count":58,"referenced_works":["https://openalex.org/W1498712972","https://openalex.org/W1585842086","https://openalex.org/W1986187395","https://openalex.org/W2021036023","https://openalex.org/W2031447968","https://openalex.org/W2045686441","https://openalex.org/W2047049848","https://openalex.org/W2097181817","https://openalex.org/W2105833837","https://openalex.org/W2111450821","https://openalex.org/W2117708954","https://openalex.org/W2130797746","https://openalex.org/W2157252460","https://openalex.org/W2161530217","https://openalex.org/W2172824072","https://openalex.org/W2300243767","https://openalex.org/W2519554845","https://openalex.org/W2559847669","https://openalex.org/W2571924096","https://openalex.org/W2591803957","https://openalex.org/W2752638378","https://openalex.org/W2796619460","https://openalex.org/W2863371389","https://openalex.org/W2889002735","https://openalex.org/W2919136764","https://openalex.org/W2934291109","https://openalex.org/W2944574328","https://openalex.org/W2949442863","https://openalex.org/W2950283170","https://openalex.org/W2956026950","https://openalex.org/W2962945174","https://openalex.org/W2963433045","https://openalex.org/W2963651557","https://openalex.org/W2963762466","https://openalex.org/W2964106292","https://openalex.org/W2970129409","https://openalex.org/W2972627332","https://openalex.org/W3044496412","https://openalex.org/W3081414434","https://openalex.org/W3099159466","https://openalex.org/W3122718520","https://openalex.org/W3166757847","https://openalex.org/W3176848035","https://openalex.org/W3183262168","https://openalex.org/W3208849091","https://openalex.org/W3215535769","https://openalex.org/W4205299417","https://openalex.org/W4221132475","https://openalex.org/W4221158809","https://openalex.org/W4226432291","https://openalex.org/W4233857083","https://openalex.org/W4281691558","https://openalex.org/W4283763988","https://openalex.org/W4285676308","https://openalex.org/W4367316093","https://openalex.org/W4387557314","https://openalex.org/W4389636963","https://openalex.org/W4394064593"],"related_works":["https://openalex.org/W2369809820","https://openalex.org/W2147278394","https://openalex.org/W2184057547","https://openalex.org/W2796321288","https://openalex.org/W2601611040","https://openalex.org/W1985854383","https://openalex.org/W2108973349","https://openalex.org/W4388257798","https://openalex.org/W2112789575","https://openalex.org/W2048163432"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"present":[2],"a":[3,115,167,226],"Virtual":[4,74],"Element":[5,75,100],"MATLAB":[6],"solver":[7,71],"for":[8,137,162,169,195,239],"elliptic":[9],"and":[10,13,21,42,53,60,67,94,133,142,185,200,204,220,244],"parabolic,":[11],"linear":[12,52],"semilinear":[14],"Partial":[15],"Differential":[16],"Equations":[17],"(PDEs)":[18],"in":[19,37,218,223],"two":[20],"three":[22,126],"space":[23,219],"dimensions,":[24],"which":[25],"is":[26,122,154],"coined":[27],"VEMcomp.":[28],"Such":[29],"PDEs":[30],"are":[31,145],"widely":[32],"applicable":[33],"to":[34],"describing":[35],"problems":[36],"material":[38],"sciences,":[39],"engineering,":[40],"cellular":[41],"developmental":[43],"biology,":[44],"among":[45],"many":[46],"other":[47],"applications.":[48],"The":[49,70],"library":[50],"covers":[51],"nonlinear":[54],"models":[55],"posed":[56],"on":[57,91],"different":[58],"simple":[59],"complex":[61],"geometries,":[62],"involving":[63],"time-dependent":[64,201],"bulk,":[65,202],"surface,":[66],"bulk-surface":[68,205],"PDEs.":[69],"employs":[72],"the":[73,98,119,157,170,182,189,209,214,241,246,256,259],"Method":[76,101],"(VEM)":[77],"of":[78,103,198,253,258],"lowest":[79],"polynomial":[80],"order":[81,104],"$${k=1}$$":[82,105],"<mml:math":[83,106],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[84,107],"<mml:mrow>":[85,108],"<mml:mi>k</mml:mi>":[86,109],"<mml:mo>=</mml:mo>":[87,110],"<mml:mn>1</mml:mn>":[88,111],"</mml:mrow>":[89,112],"</mml:math>":[90,113],"general":[92],"polygonal":[93,132],"polyhedral":[95,134],"meshes,":[96],"including":[97],"Finite":[99],"(FEM)":[102],"as":[114,147],"special":[116,148],"case":[117],"when":[118,248],"considered":[120,171,210],"mesh":[121,163,168],"simplicial.":[123],"VEMcomp":[124,130,153,179,207,233],"has":[125],"main":[127],"purposes.":[128],"First,":[129],"generates":[131],"meshes":[135,144],"optimized":[136],"fast":[138],"matrix":[139],"assembly.":[140],"Triangular":[141],"tetrahedral":[143],"encompassed":[146],"cases.":[149],"For":[150],"surface":[151,203],"PDEs,":[152,206],"compatible":[155],"with":[156,175,213,235],"well-known":[158],"Matlab":[159],"package":[160],"DistMesh":[161],"generation.":[164],"Second,":[165],"given":[166],"geometry,":[172],"possibly":[173],"generated":[174],"an":[176,230],"external":[177],"package,":[178],"computes":[180],"all":[181],"matrices":[183],"(mass":[184],"stiffness)":[186],"required":[187],"by":[188],"VEM":[190,215],"or":[191,216],"FEM":[192,217],"method.":[193],"Third,":[194],"multiple":[196],"classes":[197],"stationary":[199],"solves":[208],"PDE":[211],"problem":[212],"IMEX":[221],"Euler":[222],"time,":[224],"through":[225],"user-friendly":[227],"interface.":[228],"As":[229],"optional":[231],"post-processing,":[232],"comes":[234],"its":[236],"own":[237],"functions":[238],"plotting":[240],"numerical":[242],"solutions":[243],"evaluating":[245],"error":[247],"possible.":[249],"An":[250],"extensive":[251],"set":[252],"examples":[254],"illustrates":[255],"usage":[257],"library.":[260]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2}],"updated_date":"2026-07-09T07:52:08.696243","created_date":"2025-10-10T00:00:00"}
