{"id":"https://openalex.org/W2810477279","doi":"https://doi.org/10.1137/17m1145872","title":"Decoupling of Mixed Methods Based on Generalized Helmholtz Decompositions","display_name":"Decoupling of Mixed Methods Based on Generalized Helmholtz Decompositions","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2810477279","doi":"https://doi.org/10.1137/17m1145872","mag":"2810477279"},"language":"en","primary_location":{"id":"doi:10.1137/17m1145872","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1145872","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":true,"oa_status":"green","oa_url":"https://escholarship.org/uc/item/7bp57916","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100336427","display_name":"Long Chen","orcid":"https://orcid.org/0000-0003-0184-5446"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Long Chen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5082483290","display_name":"Xuehai Huang","orcid":"https://orcid.org/0000-0003-2966-7426"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xuehai Huang","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-2966-7426","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.202,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.76110945,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"56","issue":"5","first_page":"2796","last_page":"2825"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.998199999332428,"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":0.8634777665138245},{"id":"https://openalex.org/keywords/biharmonic-equation","display_name":"Biharmonic equation","score":0.7730740308761597},{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.6963417530059814},{"id":"https://openalex.org/keywords/superconvergence","display_name":"Superconvergence","score":0.6173801422119141},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5770927667617798},{"id":"https://openalex.org/keywords/helmholtz-free-energy","display_name":"Helmholtz free energy","score":0.5039352774620056},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.46501782536506653},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4533003866672516},{"id":"https://openalex.org/keywords/decoupling","display_name":"Decoupling (probability)","score":0.4439394176006317},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4281129240989685},{"id":"https://openalex.org/keywords/poissons-equation","display_name":"Poisson's equation","score":0.42071324586868286},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.22735640406608582},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.17993056774139404}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8634777665138245},{"id":"https://openalex.org/C145784156","wikidata":"https://www.wikidata.org/wiki/Q859808","display_name":"Biharmonic equation","level":3,"score":0.7730740308761597},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.6963417530059814},{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.6173801422119141},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5770927667617798},{"id":"https://openalex.org/C27592594","wikidata":"https://www.wikidata.org/wiki/Q865821","display_name":"Helmholtz free energy","level":2,"score":0.5039352774620056},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.46501782536506653},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4533003866672516},{"id":"https://openalex.org/C205606062","wikidata":"https://www.wikidata.org/wiki/Q5249645","display_name":"Decoupling (probability)","level":2,"score":0.4439394176006317},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4281129240989685},{"id":"https://openalex.org/C96716743","wikidata":"https://www.wikidata.org/wiki/Q827688","display_name":"Poisson's equation","level":2,"score":0.42071324586868286},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.22735640406608582},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.17993056774139404},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/17m1145872","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1145872","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:escholarship.org/ark:/13030/qt7bp57916","is_oa":true,"landing_page_url":"https://escholarship.org/uc/item/7bp57916","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"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":"SIAM Journal on Numerical Analysis, vol 56, iss 5","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:escholarship.org/ark:/13030/qt7bp57916","is_oa":true,"landing_page_url":"https://escholarship.org/uc/item/7bp57916","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"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":"SIAM Journal on Numerical Analysis, vol 56, iss 5","raw_type":"article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1722981862","display_name":null,"funder_award_id":"LY17A010010","funder_id":"https://openalex.org/F4320338464","funder_display_name":"Natural Science Foundation of Zhejiang Province"},{"id":"https://openalex.org/G1768009029","display_name":"\u5177\u6709\u5947\u6027\u7684\u591a\u7269\u7406\u573a\u8026\u5408\u7684\u7535\u78c1\u590d\u5408\u6750\u6599\u53ca\u7ed3\u6784\u7684\u591a\u5c3a\u5ea6\u6a21\u578b\u4e0e\u6570\u503c\u6a21\u62df\u65b9\u6cd5\u7814\u7a76","funder_award_id":"11671304","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2352675084","display_name":null,"funder_award_id":"LY15A010015","funder_id":"https://openalex.org/F4320338464","funder_display_name":"Natural Science Foundation of Zhejiang Province"},{"id":"https://openalex.org/G2809486088","display_name":"\u5916\u5fae\u79ef\u5206\u7406\u8bba\u53ca\u9ad8\u9636\u692d\u5706\u578b\u65b9\u7a0b\u9ad8\u6548\u6570\u503c\u7b97\u6cd5\u7684\u7814\u7a76","funder_award_id":"11771338","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4767386342","display_name":null,"funder_award_id":"DMS-1418934","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8166866937","display_name":null,"funder_award_id":"G20160019","funder_id":"https://openalex.org/F4320324224","funder_display_name":"Wenzhou Municipal Science and Technology Bureau"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320324224","display_name":"Wenzhou Municipal Science and Technology Bureau","ror":"https://ror.org/02fr0s482"},{"id":"https://openalex.org/F4320338464","display_name":"Natural Science Foundation of Zhejiang Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1489117158","https://openalex.org/W1968500177","https://openalex.org/W1969462451","https://openalex.org/W2005047411","https://openalex.org/W2024326406","https://openalex.org/W2036607335","https://openalex.org/W2049646932","https://openalex.org/W2062832849","https://openalex.org/W2075896209","https://openalex.org/W2079232547","https://openalex.org/W2113267855","https://openalex.org/W2118583977","https://openalex.org/W2122461891","https://openalex.org/W2138486270","https://openalex.org/W2143783905","https://openalex.org/W2151369319","https://openalex.org/W2164402335","https://openalex.org/W2522501703","https://openalex.org/W2547145831","https://openalex.org/W2613239920","https://openalex.org/W2614374568","https://openalex.org/W2794076570","https://openalex.org/W2962795219","https://openalex.org/W2962987095","https://openalex.org/W2963009999","https://openalex.org/W2963227054","https://openalex.org/W2964283882","https://openalex.org/W4230962563","https://openalex.org/W4232109906"],"related_works":["https://openalex.org/W2001758285","https://openalex.org/W2737775198","https://openalex.org/W2070923604","https://openalex.org/W2999089725","https://openalex.org/W4365420316","https://openalex.org/W1996232423","https://openalex.org/W3193896743","https://openalex.org/W3176862315","https://openalex.org/W3115786359","https://openalex.org/W3120022531"],"abstract_inverted_index":{"A":[0],"framework":[1],"to":[2,22,44,62],"systematically":[3,23],"decouple":[4],"high":[5],"order":[6,74],"elliptic":[7],"equations":[8,16],"into":[9],"a":[10,36,45,81],"combination":[11],"of":[12,69],"Poisson-type":[13],"and":[14,32,52,66,77],"Stokes-type":[15],"is":[17,21],"developed.":[18],"The":[19],"key":[20],"construct":[24],"the":[25,30,40,49,53,63,70],"underling":[26],"commutative":[27],"diagrams":[28],"involving":[29],"complexes":[31],"Helmholtz":[33,83],"decompositions":[34,84],"in":[35],"general":[37],"way.":[38],"Discretizing":[39],"decoupled":[41,54],"formulation":[42],"leads":[43],"natural":[46],"superconvergence":[47],"between":[48],"Galerkin":[50],"projection":[51],"approximation.":[55],"Examples":[56],"include":[57],"but":[58],"are":[59,89],"not":[60],"limited":[61],"primal":[64],"formulations":[65,68],"mixed":[67],"biharmonic":[71],"equation,":[72,76],"fourth":[73],"curl":[75],"triharmonic":[78],"equation.":[79],"As":[80],"byproduct,":[82],"for":[85],"many":[86],"dual":[87],"spaces":[88],"obtained.":[90]},"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
