{"id":"https://openalex.org/W2017629963","doi":"https://doi.org/10.1137/s0036142902417881","title":"Nonlinear Stability Analysis for the Method of Transport for the Elastic-Plastic Wave Equation","display_name":"Nonlinear Stability Analysis for the Method of Transport for the Elastic-Plastic Wave Equation","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2017629963","doi":"https://doi.org/10.1137/s0036142902417881","mag":"2017629963"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142902417881","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142902417881","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/A5046857867","display_name":"Guido Giese","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Guido Giese","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5046857867"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.13454242,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"42","issue":"6","first_page":"2569","last_page":"2589"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9976999759674072,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9976999759674072,"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":0.9976999759674072,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9972000122070312,"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":0.7415475249290466},{"id":"https://openalex.org/keywords/hyperbolic-partial-differential-equation","display_name":"Hyperbolic partial differential equation","score":0.6572722792625427},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6403977870941162},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6136974096298218},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5998489260673523},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5407178401947021},{"id":"https://openalex.org/keywords/conservation-law","display_name":"Conservation law","score":0.5123757123947144},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.503811776638031},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.4479936957359314},{"id":"https://openalex.org/keywords/wave-equation","display_name":"Wave equation","score":0.4397995173931122},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09219172596931458},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06155231595039368}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7415475249290466},{"id":"https://openalex.org/C111615704","wikidata":"https://www.wikidata.org/wiki/Q2627459","display_name":"Hyperbolic partial differential equation","level":3,"score":0.6572722792625427},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6403977870941162},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6136974096298218},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5998489260673523},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5407178401947021},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.5123757123947144},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.503811776638031},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.4479936957359314},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.4397995173931122},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09219172596931458},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06155231595039368},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036142902417881","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142902417881","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":[{"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land","score":0.5199999809265137}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W629793887","https://openalex.org/W639453929","https://openalex.org/W1555627060","https://openalex.org/W1590272204","https://openalex.org/W1595775464","https://openalex.org/W1663229168","https://openalex.org/W1689500093","https://openalex.org/W1968585714","https://openalex.org/W1970849332","https://openalex.org/W1977165692","https://openalex.org/W2004625625","https://openalex.org/W2015109371","https://openalex.org/W2065596667","https://openalex.org/W2068056613","https://openalex.org/W2100199202","https://openalex.org/W2108433712","https://openalex.org/W2140535950","https://openalex.org/W2315651828","https://openalex.org/W2468498939","https://openalex.org/W2476432869","https://openalex.org/W2519014241","https://openalex.org/W2530691799","https://openalex.org/W3003821699","https://openalex.org/W4245037559"],"related_works":["https://openalex.org/W2066764747","https://openalex.org/W2792985587","https://openalex.org/W3143691993","https://openalex.org/W4254441412","https://openalex.org/W161810272","https://openalex.org/W2969693569","https://openalex.org/W144405564","https://openalex.org/W3118471514","https://openalex.org/W2609974967","https://openalex.org/W1970322054"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"present":[4],"an":[5],"analytic":[6],"assessment":[7],"of":[8,13,17],"the":[9,14,21,34,61],"stability":[10,55,70],"and":[11,56],"convergence":[12,57],"so-called":[15],"method":[16],"transport":[18],"for":[19,52],"solving":[20],"elastic-plastic":[22],"wave":[23,37],"equation,":[24,38],"which":[25,39],"is":[26,40],"a":[27,41],"nonlinear":[28,69],"hyperbolic":[29,43],"partial":[30],"differential":[31],"equation.":[32],"For":[33,65],"purely":[35],"elastic":[36],"linear":[42],"conservation":[44],"law,":[45],"one":[46],"can":[47],"use":[48],"von":[49],"Neumann":[50],"analysis":[51],"proving":[53],"that":[54],"immediately":[58],"follow":[59],"from":[60],"Lax":[62],"equivalence":[63],"theorem.":[64],"plastic":[66],"deformation,":[67],"however,":[68],"proofs":[71],"require":[72],"greater":[73],"effort.":[74]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}