{"id":"https://openalex.org/W2002182424","doi":"https://doi.org/10.1137/s0036142903435235","title":"Convergent Difference Schemes for Degenerate Elliptic and Parabolic Equations: Hamilton--Jacobi Equations and Free Boundary Problems","display_name":"Convergent Difference Schemes for Degenerate Elliptic and Parabolic Equations: Hamilton--Jacobi Equations and Free Boundary Problems","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2002182424","doi":"https://doi.org/10.1137/s0036142903435235","mag":"2002182424"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142903435235","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142903435235","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/A5004824330","display_name":"Adam M. Oberman","orcid":"https://orcid.org/0000-0002-4214-7364"},"institutions":[{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Adam M. Oberman","raw_affiliation_strings":["Simon Fraser University"],"affiliations":[{"raw_affiliation_string":"Simon Fraser University","institution_ids":["https://openalex.org/I18014758"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5004824330"],"corresponding_institution_ids":["https://openalex.org/I18014758"],"apc_list":null,"apc_paid":null,"fwci":2.871,"has_fulltext":false,"cited_by_count":195,"citation_normalized_percentile":{"value":0.91173061,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"44","issue":"2","first_page":"879","last_page":"895"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9908999800682068,"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9894000291824341,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8710355758666992},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.5916752815246582},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.5382724404335022},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5325844287872314},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.5264202952384949},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.5170201063156128},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4960835874080658},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.494401216506958},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.48147502541542053},{"id":"https://openalex.org/keywords/obstacle-problem","display_name":"Obstacle problem","score":0.47223448753356934},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.41550391912460327},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41353312134742737},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.37688714265823364}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8710355758666992},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5916752815246582},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.5382724404335022},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5325844287872314},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.5264202952384949},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.5170201063156128},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4960835874080658},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.494401216506958},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.48147502541542053},{"id":"https://openalex.org/C132369183","wikidata":"https://www.wikidata.org/wiki/Q3406250","display_name":"Obstacle problem","level":3,"score":0.47223448753356934},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.41550391912460327},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41353312134742737},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.37688714265823364},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036142903435235","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142903435235","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W153353184","https://openalex.org/W1487586009","https://openalex.org/W1505284970","https://openalex.org/W1986838484","https://openalex.org/W1996123578","https://openalex.org/W1997221482","https://openalex.org/W1999545889","https://openalex.org/W2002707718","https://openalex.org/W2003009438","https://openalex.org/W2014405238","https://openalex.org/W2018299815","https://openalex.org/W2025073461","https://openalex.org/W2026073961","https://openalex.org/W2027438381","https://openalex.org/W2032316144","https://openalex.org/W2034939914","https://openalex.org/W2053068479","https://openalex.org/W2054113582","https://openalex.org/W2056826596","https://openalex.org/W2066501150","https://openalex.org/W2076091926","https://openalex.org/W2082437368","https://openalex.org/W2084406624","https://openalex.org/W2089633435","https://openalex.org/W2092046358","https://openalex.org/W2116729868","https://openalex.org/W2125671914","https://openalex.org/W2147786048","https://openalex.org/W2177195156","https://openalex.org/W2335457376","https://openalex.org/W2471986815","https://openalex.org/W2482978852","https://openalex.org/W2487508536","https://openalex.org/W3021722416","https://openalex.org/W4212960264","https://openalex.org/W4292069163","https://openalex.org/W4297084762"],"related_works":["https://openalex.org/W1489292980","https://openalex.org/W2951610245","https://openalex.org/W2795079910","https://openalex.org/W1430963189","https://openalex.org/W2052430123","https://openalex.org/W3037410748","https://openalex.org/W4319835971","https://openalex.org/W2049901819","https://openalex.org/W1983437306","https://openalex.org/W1974262772"],"abstract_inverted_index":{"Convergent":[0],"numerical":[1],"schemes":[2,23,33],"for":[3,42,59,88],"degenerate":[4],"elliptic":[5],"partial":[6],"differential":[7],"equations":[8,44,51,63],"are":[9,15,24,40,46,64,71,100,105],"constructed":[10],"and":[11,26,45,54,61,83,97,102],"implemented.":[12],"Simple":[13],"conditions":[14],"identified":[16],"which":[17,78],"ensure":[18],"that":[19],"nonlinear":[20],"finite":[21],"difference":[22],"monotone":[25],"nonexpansive":[27],"in":[28],"the":[29],"maximum":[30],"norm.":[31],"Explicit":[32,53],"endowed":[34],"with":[35],"an":[36],"explicit":[37],"CFL":[38],"condition":[39],"built":[41,101],"time-dependent":[43],"used":[47],"to":[48],"solve":[49],"stationary":[50],"iteratively.":[52],"implicit":[55],"formulations":[56],"of":[57,69,75],"monotonicity":[58],"first-":[60],"second-order":[62],"unified.":[65],"Bounds":[66],"on":[67],"orders":[68],"accuracy":[70],"established.":[72],"An":[73],"example":[74],"a":[76],"scheme":[77],"is":[79,85],"stable,":[80],"but":[81],"nonmonotone":[82],"nonconvergent,":[84],"presented.":[86,106],"Schemes":[87],"Hamilton--Jacobi":[89],"equations,":[90],"obstacle":[91],"problems,":[92,96],"one-phase":[93],"free":[94],"boundary":[95],"stochastic":[98],"games":[99],"computational":[103],"results":[104]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":18},{"year":2020,"cited_by_count":14},{"year":2019,"cited_by_count":21},{"year":2018,"cited_by_count":15},{"year":2017,"cited_by_count":14},{"year":2016,"cited_by_count":18},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":12},{"year":2012,"cited_by_count":6}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
