{"id":"https://openalex.org/W2213951665","doi":"https://doi.org/10.1137/15m1013651","title":"A New Discretization for $m$th-Laplace Equations with Arbitrary Polynomial Degrees","display_name":"A New Discretization for $m$th-Laplace Equations with Arbitrary Polynomial Degrees","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2213951665","doi":"https://doi.org/10.1137/15m1013651","mag":"2213951665"},"language":"en","primary_location":{"id":"doi:10.1137/15m1013651","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1013651","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/1512.06513","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031200453","display_name":"Mira Schedensack","orcid":"https://orcid.org/0000-0003-1182-9116"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"M. Schedensack","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5031200453"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00280188,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"54","issue":"4","first_page":"2138","last_page":"2162"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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":0.9955999851226807,"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":0.8070682287216187},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6841105222702026},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6396142840385437},{"id":"https://openalex.org/keywords/degree-of-a-polynomial","display_name":"Degree of a polynomial","score":0.6021947860717773},{"id":"https://openalex.org/keywords/ansatz","display_name":"Ansatz","score":0.5808938145637512},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5796664953231812},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5020925998687744},{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.49779272079467773},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3861587941646576},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32850125432014465},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.10890308022499084},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.08847606182098389}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8070682287216187},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6841105222702026},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6396142840385437},{"id":"https://openalex.org/C25878781","wikidata":"https://www.wikidata.org/wiki/Q1473607","display_name":"Degree of a polynomial","level":3,"score":0.6021947860717773},{"id":"https://openalex.org/C130979935","wikidata":"https://www.wikidata.org/wiki/Q568954","display_name":"Ansatz","level":2,"score":0.5808938145637512},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5796664953231812},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5020925998687744},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.49779272079467773},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3861587941646576},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32850125432014465},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.10890308022499084},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.08847606182098389}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/15m1013651","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1013651","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:1512.06513","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1512.06513","pdf_url":"https://arxiv.org/pdf/1512.06513","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2213951665","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1512.06513.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:uni-augsburg.opus-bayern.de:88998","is_oa":false,"landing_page_url":"https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/88998","pdf_url":null,"source":{"id":"https://openalex.org/S4306400930","display_name":"OPUS (Augsburg University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119916105","host_organization_name":"Augsburg University","host_organization_lineage":["https://openalex.org/I119916105"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"},{"id":"doi:10.48550/arxiv.1512.06513","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1512.06513","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:1512.06513","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1512.06513","pdf_url":"https://arxiv.org/pdf/1512.06513","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2213951665.pdf","grobid_xml":"https://content.openalex.org/works/W2213951665.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W325210746","https://openalex.org/W592911714","https://openalex.org/W1585767079","https://openalex.org/W1604809219","https://openalex.org/W1708679080","https://openalex.org/W1759234922","https://openalex.org/W1990225789","https://openalex.org/W1993179343","https://openalex.org/W1998903284","https://openalex.org/W2009985306","https://openalex.org/W2035654636","https://openalex.org/W2041523977","https://openalex.org/W2044959876","https://openalex.org/W2048407683","https://openalex.org/W2062819342","https://openalex.org/W2082131680","https://openalex.org/W2082866666","https://openalex.org/W2084743165","https://openalex.org/W2094648722","https://openalex.org/W2107813568","https://openalex.org/W2168893189","https://openalex.org/W2322259286","https://openalex.org/W2408886290","https://openalex.org/W2522501703","https://openalex.org/W2592623476"],"related_works":["https://openalex.org/W2052526235","https://openalex.org/W3139511031","https://openalex.org/W3125331871","https://openalex.org/W1506381275","https://openalex.org/W2539058769","https://openalex.org/W2041781096","https://openalex.org/W2759216205","https://openalex.org/W2787098163","https://openalex.org/W2183497817","https://openalex.org/W2104341945","https://openalex.org/W2094648722","https://openalex.org/W2163995396","https://openalex.org/W2469579286","https://openalex.org/W3194129446","https://openalex.org/W2766590360","https://openalex.org/W1987969517","https://openalex.org/W2144586796","https://openalex.org/W3095371466","https://openalex.org/W2760869208","https://openalex.org/W3148833448"],"abstract_inverted_index":{"This":[0],"paper":[1,96],"introduces":[2],"new":[3,28,106],"mixed":[4],"formulations":[5],"and":[6,38,49,53,71,91],"discretizations":[7,29,66],"for":[8,16,24,31,51,56,75,82,101,104],"$m$th-Laplace":[9],"equations":[10],"of":[11,34,47,54,68],"the":[12,39,44,59,64,88,105],"form":[13],"$(-1)^m\\Delta^m":[14],"u=f$":[15],"arbitrary":[17,35,83],"$m=1,2,3,\\dots$":[18],"based":[19],"on":[20],"novel":[21],"Helmholtz-type":[22],"decompositions":[23],"tensor-valued":[25],"functions.":[26],"The":[27],"allow":[30],"ansatz":[32],"spaces":[33],"polynomial":[36],"degree":[37],"lowest-order":[40,65],"choice":[41],"coincides":[42],"with":[43],"nonconforming":[45],"FEMs":[46],"Crouzeix":[48],"Raviart":[50],"$m=1$":[52],"Morley":[55],"$m=2$.":[57],"Since":[58],"derivatives":[60],"are":[61],"directly":[62],"approximated,":[63],"consist":[67],"piecewise":[69,72],"affine":[70],"constant":[73],"functions":[74],"any":[76],"$m=1,2,\\dots.$":[77],"Moreover,":[78],"a":[79,89,92],"uniform":[80],"implementation":[81],"$m$":[84],"is":[85],"possible.":[86],"Besides":[87],"priori":[90],"posteriori":[93],"analysis,":[94],"this":[95],"proves":[97],"optimal":[98],"convergence":[99],"rates":[100],"adaptive":[102],"algorithms":[103],"discretizations.":[107]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
