{"id":"https://openalex.org/W1988384447","doi":"https://doi.org/10.1137/050632932","title":"Convergence Rate of Monotone Numerical Schemes for Hamilton\u2013Jacobi Equations with Weak Boundary Conditions","display_name":"Convergence Rate of Monotone Numerical Schemes for Hamilton\u2013Jacobi Equations with Weak Boundary Conditions","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W1988384447","doi":"https://doi.org/10.1137/050632932","mag":"1988384447"},"language":"en","primary_location":{"id":"doi:10.1137/050632932","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050632932","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/A5089424158","display_name":"Knut Waagan","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Knut Waagan","raw_affiliation_strings":["knut.waagan@cma.uio.no#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"knut.waagan@cma.uio.no#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5089424158"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.08853641,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"46","issue":"5","first_page":"2371","last_page":"2392"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.9901999831199646,"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"}},{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.9837999939918518,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.9203604459762573},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.7173174619674683},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.691428542137146},{"id":"https://openalex.org/keywords/hamilton\u2013jacobi-equation","display_name":"Hamilton\u2013Jacobi equation","score":0.6636661887168884},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5425111055374146},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5359746813774109},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.5298362374305725},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5205194354057312},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.5190104246139526},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5133582949638367},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.4881187379360199},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.4721011221408844},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3377417325973511},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16564199328422546},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.0835610032081604}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9203604459762573},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.7173174619674683},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.691428542137146},{"id":"https://openalex.org/C2778860007","wikidata":"https://www.wikidata.org/wiki/Q1060137","display_name":"Hamilton\u2013Jacobi equation","level":2,"score":0.6636661887168884},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5425111055374146},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5359746813774109},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.5298362374305725},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5205194354057312},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.5190104246139526},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5133582949638367},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.4881187379360199},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.4721011221408844},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3377417325973511},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16564199328422546},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.0835610032081604},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"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/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/050632932","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050632932","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:CiteSeerX.psu:10.1.1.230.741","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.230.741","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ntnu.no/conservation/2006/048.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W29297237","https://openalex.org/W153353184","https://openalex.org/W1487586009","https://openalex.org/W1549045256","https://openalex.org/W1558902221","https://openalex.org/W1939243400","https://openalex.org/W1986838484","https://openalex.org/W2005880875","https://openalex.org/W2025438169","https://openalex.org/W2027438381","https://openalex.org/W2032316144","https://openalex.org/W2042112368","https://openalex.org/W2091365439","https://openalex.org/W2125244837","https://openalex.org/W2177195156","https://openalex.org/W2749408143","https://openalex.org/W4247347880","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W3185235544","https://openalex.org/W2897842840","https://openalex.org/W2911623553","https://openalex.org/W2758222473","https://openalex.org/W2807723500","https://openalex.org/W3098536285","https://openalex.org/W4362515624","https://openalex.org/W4313447529","https://openalex.org/W4200632674","https://openalex.org/W2071077531"],"abstract_inverted_index":{"We":[0,17,83],"study":[1],"a":[2,19,51,58,86,101],"class":[3],"of":[4,22,61,71,92],"monotone":[5],"numerical":[6],"schemes":[7],"for":[8,54],"time-dependent":[9],"Hamilton\u2013Jacobi":[10],"equations":[11],"with":[12],"weak":[13],"Dirichlet":[14],"boundary":[15,41,78,109],"conditions.":[16,110],"get":[18],"convergence":[20],"rate":[21],"$\\frac{1}{2}$":[23],"under":[24],"some":[25],"usual":[26],"assumptions":[27],"on":[28,35],"the":[29,36,40,45,69,72,77,80,93,107],"data,":[30],"plus":[31],"an":[32,97],"extra":[33],"assumption":[34],"Hamiltonian":[37],"$H(Du,x)$":[38],"at":[39,76],"$\\partial\\Omega$.":[42],"More":[43],"specifically":[44],"mapping":[46],"$p\\to":[47],"H(p,x)$":[48],"must":[49],"satisfy":[50],"monotonicity":[52],"condition":[53,67],"all":[55],"p":[56],"in":[57,79],"certain":[59],"subset":[60],"$\\mathbf{R}^n$":[62],"given":[63],"by":[64],"$\\Omega$.":[65],"This":[66],"allows":[68],"use":[70],"interior":[73],"subsolution":[74],"conditions":[75],"comparison":[81,87],"arguments.":[82],"also":[84],"prove":[85],"result":[88],"and":[89],"Lipschitz":[90],"regularity":[91],"exact":[94],"solution.":[95],"As":[96],"example":[98],"we":[99],"construct":[100],"Godunov-type":[102],"scheme":[103],"that":[104],"can":[105],"handle":[106],"weakened":[108]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}