{"id":"https://openalex.org/W184276028","doi":"https://doi.org/10.1137/s0036142902402158","title":"The <i>P</i><sub>1</sub><sup><i>mod</i></sup> Element: A New Nonconforming Finite Element for Convection-Diffusion Problems","display_name":"The <i>P</i><sub>1</sub><sup><i>mod</i></sup> Element: A New Nonconforming Finite Element for Convection-Diffusion Problems","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W184276028","doi":"https://doi.org/10.1137/s0036142902402158","mag":"184276028"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142902402158","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142902402158","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":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017304368","display_name":"Petr Knobloch","orcid":"https://orcid.org/0000-0003-2709-5882"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Petr Knobloch","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5053874836","display_name":"Lutz Tobiska","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lutz Tobiska","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.6605,"has_fulltext":false,"cited_by_count":38,"citation_normalized_percentile":{"value":0.91660703,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"41","issue":"2","first_page":"436","last_page":"456"},"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":0.9998999834060669,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","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"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9951000213623047,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8437970876693726},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7695921659469604},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5648022890090942},{"id":"https://openalex.org/keywords/convection\u2013diffusion-equation","display_name":"Convection\u2013diffusion equation","score":0.5108413100242615},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5087490677833557},{"id":"https://openalex.org/keywords/bilinear-form","display_name":"Bilinear form","score":0.5067973732948303},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.506098210811615},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.4933880865573883},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.49099424481391907},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.4792499542236328},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.4605492949485779},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38839420676231384},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3387947976589203},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09705886244773865}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8437970876693726},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7695921659469604},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5648022890090942},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.5108413100242615},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5087490677833557},{"id":"https://openalex.org/C8828549","wikidata":"https://www.wikidata.org/wiki/Q837924","display_name":"Bilinear form","level":2,"score":0.5067973732948303},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.506098210811615},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.4933880865573883},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.49099424481391907},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.4792499542236328},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.4605492949485779},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38839420676231384},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3387947976589203},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09705886244773865},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036142902402158","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142902402158","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:CiteSeerX.psu:10.1.1.560.7881","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.560.7881","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.karlin.mff.cuni.cz/~knobloch/PAPERS/40215.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W79873316","https://openalex.org/W1963604048","https://openalex.org/W1984103037","https://openalex.org/W2007322777","https://openalex.org/W2011185352","https://openalex.org/W2061074558","https://openalex.org/W2074772185","https://openalex.org/W2095399846","https://openalex.org/W2117053242","https://openalex.org/W2145344822","https://openalex.org/W4238437064"],"related_works":["https://openalex.org/W2927373829","https://openalex.org/W2354715440","https://openalex.org/W4234704706","https://openalex.org/W4299625300","https://openalex.org/W2808682125","https://openalex.org/W2073705841","https://openalex.org/W2168805210","https://openalex.org/W2023166590","https://openalex.org/W2900949317","https://openalex.org/W3004639085"],"abstract_inverted_index":{"We":[0],"consider":[1],"a":[2,65,79,95],"nonconforming":[3,27,67],"streamline":[4,21,96],"diffusion":[5,22,97],"finite":[6,28,70],"element":[7,29,71,92],"method":[8,23],"for":[9,48],"solving":[10],"convection-diffusion":[11],"problems.":[12],"The":[13],"loss":[14],"of":[15,19,82,89,110],"the":[16,20,45,49,60,104,107,111],"Galerkin":[17],"orthogonality":[18],"when":[24],"applied":[25,93],"to":[26,44,94],"approximations":[30],"results":[31],"in":[32],"an":[33],"additional":[34],"error":[35,87],"term":[36],"which":[37],"cannot":[38],"be":[39],"estimated":[40],"uniformly":[41],"with":[42],"respect":[43],"perturbation":[46],"parameter":[47],"standard":[50],"piecewise":[51],"linear":[52],"or":[53],"rotated":[54],"bilinear":[55],"elements.":[56],"Therefore,":[57],"starting":[58],"from":[59],"Crouzeix--Raviart":[61],"element,":[62],"we":[63],"construct":[64],"modified":[66],"first":[68],"order":[69],"space":[72],"on":[73],"shape":[74],"regular":[75],"triangular":[76],"meshes":[77],"satisfying":[78],"patch":[80],"test":[81],"higher":[83],"order.":[84],"A":[85],"rigorous":[86],"analysis":[88],"this":[90],"P1mod":[91],"discretization":[98],"is":[99],"given.The":[100],"numerical":[101],"tests":[102],"show":[103],"robustness":[105],"and":[106],"high":[108],"accuracy":[109],"new":[112],"method.":[113]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}