{"id":"https://openalex.org/W1996885477","doi":"https://doi.org/10.1137/06067119x","title":"Discontinuous Galerkin Finite Element Approximation of Nonlinear Second-Order Elliptic and Hyperbolic Systems","display_name":"Discontinuous Galerkin Finite Element Approximation of Nonlinear Second-Order Elliptic and Hyperbolic Systems","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W1996885477","doi":"https://doi.org/10.1137/06067119x","mag":"1996885477"},"language":"en","primary_location":{"id":"doi:10.1137/06067119x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/06067119x","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/A5061841111","display_name":"Christoph Ortner","orcid":"https://orcid.org/0000-0003-1498-8120"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Christoph Ortner","raw_affiliation_strings":["University of Oxford"],"affiliations":[{"raw_affiliation_string":"University of Oxford","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064002486","display_name":"Endre S\u00fcli","orcid":"https://orcid.org/0000-0002-0812-6105"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Endre S\u00fcli","raw_affiliation_strings":["University of Oxford, Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, United Kingdom"],"affiliations":[{"raw_affiliation_string":"University of Oxford, Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, United Kingdom","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5061841111"],"corresponding_institution_ids":["https://openalex.org/I40120149"],"apc_list":null,"apc_paid":null,"fwci":4.7132,"has_fulltext":false,"cited_by_count":64,"citation_normalized_percentile":{"value":0.94414702,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"45","issue":"4","first_page":"1370","last_page":"1397"},"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":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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9997000098228455,"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/T10514","display_name":"Numerical methods in engineering","score":0.9994000196456909,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8727189302444458},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.6684781908988953},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6080061793327332},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5423802137374878},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.5234414935112},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.49128884077072144},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.488505482673645},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4312064051628113},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.42043018341064453},{"id":"https://openalex.org/keywords/lipschitz-domain","display_name":"Lipschitz domain","score":0.4199659526348114}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8727189302444458},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.6684781908988953},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6080061793327332},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5423802137374878},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.5234414935112},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.49128884077072144},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.488505482673645},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4312064051628113},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.42043018341064453},{"id":"https://openalex.org/C13474197","wikidata":"https://www.wikidata.org/wiki/Q1158876","display_name":"Lipschitz domain","level":3,"score":0.4199659526348114},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1137/06067119x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/06067119x","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:wrap.warwick.ac.uk:60413","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400665","display_name":"Warwick Research Archive Portal (University of Warwick)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39555362","host_organization_name":"University of Warwick","host_organization_lineage":["https://openalex.org/I39555362"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.154.5882","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.154.5882","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://web.comlab.ox.ac.uk/people/endre.suli/elasticitySIAM.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.227.4000","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.227.4000","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://eprints.maths.ox.ac.uk/1118/1/NA-06-05.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.718.9201","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.718.9201","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://homepages.warwick.ac.uk/staff/C.Ortner/pdfs/2007-SINUM-DGFEM.pdf","raw_type":"text"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:7b96ae31-5d6c-4cc7-90e2-2e3a07e63822","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:7b96ae31-5d6c-4cc7-90e2-2e3a07e63822","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://eprints.maths.ox.ac.uk/1118","raw_type":"Report"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:c01c0731-8c3d-43b9-a6d3-5ba1a00a2178","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:c01c0731-8c3d-43b9-a6d3-5ba1a00a2178","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symplectic Elements at Oxford","raw_type":"Journal article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.550000011920929,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W122839734","https://openalex.org/W1508861003","https://openalex.org/W1524015806","https://openalex.org/W1600997507","https://openalex.org/W1604436244","https://openalex.org/W1966513386","https://openalex.org/W1975505063","https://openalex.org/W1979771104","https://openalex.org/W1991960225","https://openalex.org/W2012701400","https://openalex.org/W2041523977","https://openalex.org/W2042816276","https://openalex.org/W2071928229","https://openalex.org/W2082741499","https://openalex.org/W2102096503","https://openalex.org/W2103320720","https://openalex.org/W2130350269","https://openalex.org/W2136256106","https://openalex.org/W2157715842","https://openalex.org/W2415509676"],"related_works":["https://openalex.org/W2087110602","https://openalex.org/W2161399929","https://openalex.org/W2110693695","https://openalex.org/W2764244586","https://openalex.org/W2043686470","https://openalex.org/W2096756136","https://openalex.org/W2080994790","https://openalex.org/W1590663584","https://openalex.org/W3032262642","https://openalex.org/W4380686240"],"abstract_inverted_index":{"We":[0],"develop":[1],"the":[2,45,53,61,75],"convergence":[3],"analysis":[4],"of":[5,19,60],"discontinuous":[6],"Galerkin":[7],"finite":[8],"element":[9],"approximations":[10],"to":[11,34],"symmetric":[12],"second-order":[13],"quasi-linear":[14],"elliptic":[15],"and":[16,68],"hyperbolic":[17],"systems":[18],"partial":[20],"differential":[21],"equations":[22],"in":[23,26,31,48,74],"divergence":[24],"form":[25],"a":[27,69],"bounded":[28],"spatial":[29],"domain":[30],"$\\mathbb{R}^d$,":[32],"subject":[33],"mixed":[35],"Dirichlet\u2013Neumann":[36],"boundary":[37],"conditions.":[38],"Optimal-order":[39],"asymptotic":[40],"bounds":[41],"are":[42,72],"derived":[43],"on":[44],"discretization":[46],"error":[47],"each":[49],"case":[50],"without":[51],"requiring":[52],"global":[54],"Lipschitz":[55],"continuity":[56],"or":[57],"uniform":[58],"monotonicity":[59],"stress":[62],"tensor.":[63],"Instead,":[64],"only":[65],"local":[66],"smoothness":[67],"G\u00e5rding":[70],"inequality":[71],"used":[73],"analysis.":[76]},"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":1},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":6}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
