{"id":"https://openalex.org/W2596129588","doi":"https://doi.org/10.1090/mcom/3265","title":"A kernel-based discretisation method for first order partial differential equations","display_name":"A kernel-based discretisation method for first order partial differential equations","publication_year":2017,"publication_date":"2017-03-16","ids":{"openalex":"https://openalex.org/W2596129588","doi":"https://doi.org/10.1090/mcom/3265","mag":"2596129588"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3265","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3265","pdf_url":"https://www.ams.org/mcom/2018-87-312/S0025-5718-2017-03265-8/S0025-5718-2017-03265-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2018-87-312/S0025-5718-2017-03265-8/S0025-5718-2017-03265-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031442008","display_name":"Tobias Ramming","orcid":null},"institutions":[{"id":"https://openalex.org/I54009628","display_name":"University of Bayreuth","ror":"https://ror.org/0234wmv40","country_code":"DE","type":"education","lineage":["https://openalex.org/I54009628"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Tobias Ramming","raw_affiliation_strings":["Department of Mathematics, University of Bayreuth, D-95440 Bayreuth, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Bayreuth, D-95440 Bayreuth, Germany","institution_ids":["https://openalex.org/I54009628"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066096555","display_name":"Holger Wendland","orcid":"https://orcid.org/0000-0002-9614-5321"},"institutions":[{"id":"https://openalex.org/I54009628","display_name":"University of Bayreuth","ror":"https://ror.org/0234wmv40","country_code":"DE","type":"education","lineage":["https://openalex.org/I54009628"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Holger Wendland","raw_affiliation_strings":["Department of Mathematics, University of Bayreuth, D-95440 Bayreuth, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Bayreuth, D-95440 Bayreuth, Germany","institution_ids":["https://openalex.org/I54009628"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5031442008"],"corresponding_institution_ids":["https://openalex.org/I54009628"],"apc_list":null,"apc_paid":null,"fwci":0.9877,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.72788856,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"87","issue":"312","first_page":"1757","last_page":"1781"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11694","display_name":"Fluid Dynamics Simulations and Interactions","score":1.0,"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/T11694","display_name":"Fluid Dynamics Simulations and Interactions","score":1.0,"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":0.9975000023841858,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9768000245094299,"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/mathematics","display_name":"Mathematics","score":0.8185713291168213},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.795480489730835},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.7130551338195801},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6400632858276367},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.6332658529281616},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5729097127914429},{"id":"https://openalex.org/keywords/smoothed-particle-hydrodynamics","display_name":"Smoothed-particle hydrodynamics","score":0.5428171157836914},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5426680445671082},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.46853938698768616},{"id":"https://openalex.org/keywords/order-of-accuracy","display_name":"Order of accuracy","score":0.44681715965270996},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.42836394906044006},{"id":"https://openalex.org/keywords/method-of-characteristics","display_name":"Method of characteristics","score":0.2133176326751709},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08479410409927368}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8185713291168213},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.795480489730835},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.7130551338195801},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6400632858276367},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6332658529281616},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5729097127914429},{"id":"https://openalex.org/C122564879","wikidata":"https://www.wikidata.org/wiki/Q733073","display_name":"Smoothed-particle hydrodynamics","level":2,"score":0.5428171157836914},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5426680445671082},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46853938698768616},{"id":"https://openalex.org/C39177556","wikidata":"https://www.wikidata.org/wiki/Q7100567","display_name":"Order of accuracy","level":4,"score":0.44681715965270996},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.42836394906044006},{"id":"https://openalex.org/C33163149","wikidata":"https://www.wikidata.org/wiki/Q1785085","display_name":"Method of characteristics","level":3,"score":0.2133176326751709},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08479410409927368},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"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/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/mcom/3265","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3265","pdf_url":"https://www.ams.org/mcom/2018-87-312/S0025-5718-2017-03265-8/S0025-5718-2017-03265-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai::55240","is_oa":false,"landing_page_url":"https://eref.uni-bayreuth.de/55240/","pdf_url":null,"source":{"id":"https://openalex.org/S4377196442","display_name":"ERef Bayreuth (University of Bayreuth)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I54009628","host_organization_name":"University of Bayreuth","host_organization_lineage":["https://openalex.org/I54009628"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Artikel in einer Zeitschrift"}],"best_oa_location":{"id":"doi:10.1090/mcom/3265","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3265","pdf_url":"https://www.ams.org/mcom/2018-87-312/S0025-5718-2017-03265-8/S0025-5718-2017-03265-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2596129588.pdf","grobid_xml":"https://content.openalex.org/works/W2596129588.grobid-xml"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W187557541","https://openalex.org/W320449047","https://openalex.org/W587977125","https://openalex.org/W1486164486","https://openalex.org/W1507957971","https://openalex.org/W1509925099","https://openalex.org/W1575011268","https://openalex.org/W1597405158","https://openalex.org/W1964130785","https://openalex.org/W1968816607","https://openalex.org/W1972685235","https://openalex.org/W1980944938","https://openalex.org/W1983195644","https://openalex.org/W2012205781","https://openalex.org/W2020298878","https://openalex.org/W2022694751","https://openalex.org/W2023606182","https://openalex.org/W2030738345","https://openalex.org/W2034976587","https://openalex.org/W2044602433","https://openalex.org/W2051781990","https://openalex.org/W2051782216","https://openalex.org/W2053567007","https://openalex.org/W2068434577","https://openalex.org/W2069438562","https://openalex.org/W2086920325","https://openalex.org/W2092005534","https://openalex.org/W2100636165","https://openalex.org/W2115370654","https://openalex.org/W2115520718","https://openalex.org/W2127689830","https://openalex.org/W2131057369","https://openalex.org/W2148502234","https://openalex.org/W2216485242","https://openalex.org/W2222833901","https://openalex.org/W2316806696","https://openalex.org/W2337104636","https://openalex.org/W4233613753","https://openalex.org/W4244681853","https://openalex.org/W4244809089","https://openalex.org/W4251512373"],"related_works":["https://openalex.org/W4212986122","https://openalex.org/W2943982390","https://openalex.org/W3186772962","https://openalex.org/W4287068106","https://openalex.org/W2256457273","https://openalex.org/W3189786893","https://openalex.org/W4206887663","https://openalex.org/W4298764231","https://openalex.org/W2596129588","https://openalex.org/W4287185834"],"abstract_inverted_index":{"We":[0,58],"derive":[1],"a":[2,18,36,55,111,122],"new":[3],"discretisation":[4],"method":[5,47,117],"for":[6,63],"first":[7],"order":[8,81],"PDEs":[9],"of":[10,76,90,100,121],"arbitrary":[11,105],"spatial":[12,20,23],"dimension,":[13],"which":[14],"is":[15,25,35],"based":[16],"upon":[17],"meshfree":[19],"approximation.":[21],"This":[22],"approximation":[24,80],"similar":[26],"to":[27],"the":[28,45,64,73,77,84,88,91,119],"SPH":[29,46],"(smoothed":[30],"particle":[31],"hydrodynamics)":[32],"technique":[33],"and":[34,53,61,87],"typical":[37],"kernel-based":[38],"method.":[39],"It":[40],"differs,":[41],"however,":[42],"significantly":[43],"from":[44],"since":[48],"it":[49],"employs":[50],"an":[51,97],"Eulerian":[52],"not":[54],"Lagrangian":[56],"approach.":[57],"prove":[59],"stability":[60],"convergence":[62,106],"resulting":[65],"semi-discrete":[66],"scheme":[67],"under":[68],"certain":[69],"smoothness":[70,89],"assumptions":[71],"on":[72,83],"defining":[74],"function":[75],"PDE.":[78],"The":[79],"depends":[82],"underlying":[85],"kernel":[86],"solution.":[92],"Hence,":[93],"we":[94,109],"also":[95],"review":[96],"easy":[98],"way":[99],"constructing":[101],"smooth":[102],"kernels":[103],"yielding":[104],"orders.":[107],"Finally,":[108],"give":[110],"numerical":[112],"example":[113],"by":[114],"testing":[115],"our":[116],"in":[118],"case":[120],"one-dimensional":[123],"Burgers":[124],"equation.":[125]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}