{"id":"https://openalex.org/W1967053584","doi":"https://doi.org/10.1090/s0025-5718-06-01875-8","title":"Order of convergence of second order schemes based on the minmod limiter","display_name":"Order of convergence of second order schemes based on the minmod limiter","publication_year":2006,"publication_date":"2006-05-23","ids":{"openalex":"https://openalex.org/W1967053584","doi":"https://doi.org/10.1090/s0025-5718-06-01875-8","mag":"1967053584"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-06-01875-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-06-01875-8","pdf_url":"https://www.ams.org/mcom/2006-75-256/S0025-5718-06-01875-8/S0025-5718-06-01875-8.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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","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":"hybrid","oa_url":"https://www.ams.org/mcom/2006-75-256/S0025-5718-06-01875-8/S0025-5718-06-01875-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001592507","display_name":"Bojan Popov","orcid":"https://orcid.org/0000-0002-6837-2404"},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Bojan Popov","raw_affiliation_strings":["Department of Mathematics, Texas A&M University, College Station, Texas 77845"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Texas A&M University, College Station, Texas 77845","institution_ids":["https://openalex.org/I91045830"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065821489","display_name":"Ognian Trifonov","orcid":null},"institutions":[{"id":"https://openalex.org/I155781252","display_name":"University of South Carolina","ror":"https://ror.org/02b6qw903","country_code":"US","type":"education","lineage":["https://openalex.org/I155781252"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ognian Trifonov","raw_affiliation_strings":["Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208","Department of Mathematics; University of South Carolina; Columbia South Carolina 29208"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208","institution_ids":["https://openalex.org/I155781252"]},{"raw_affiliation_string":"Department of Mathematics; University of South Carolina; Columbia South Carolina 29208","institution_ids":["https://openalex.org/I155781252"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5001592507"],"corresponding_institution_ids":["https://openalex.org/I91045830"],"apc_list":null,"apc_paid":null,"fwci":0.4526,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.60408876,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"75","issue":"256","first_page":"1735","last_page":"1753"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9997000098228455,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9990000128746033,"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":0.9983000159263611,"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/algorithm","display_name":"Algorithm","score":0.7259583473205566},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4471207857131958},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.38761743903160095},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3289368748664856}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.7259583473205566},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4471207857131958},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.38761743903160095},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3289368748664856}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/s0025-5718-06-01875-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-06-01875-8","pdf_url":"https://www.ams.org/mcom/2006-75-256/S0025-5718-06-01875-8/S0025-5718-06-01875-8.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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.154.1759","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.154.1759","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2006-75-256/S0025-5718-06-01875-8/S0025-5718-06-01875-8.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.484.7620","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.484.7620","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.tamu.edu/~popov/minmod2.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-06-01875-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-06-01875-8","pdf_url":"https://www.ams.org/mcom/2006-75-256/S0025-5718-06-01875-8/S0025-5718-06-01875-8.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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G51245283","display_name":"NONLINEAR FINITE ELEMENT APPROXIMATION OF FIRST-ORDER PDE'S IN L1","funder_award_id":"0510650","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7917516974","display_name":"Estimating the Number of Lattice Points Close to a Curve","funder_award_id":"9970455","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1967053584.pdf","grobid_xml":"https://content.openalex.org/works/W1967053584.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1972759058","https://openalex.org/W1975706278","https://openalex.org/W1987418883","https://openalex.org/W1992812527","https://openalex.org/W2003705956","https://openalex.org/W2008076987","https://openalex.org/W2008077484","https://openalex.org/W2014251809","https://openalex.org/W2020168202","https://openalex.org/W2023421695","https://openalex.org/W2026073961","https://openalex.org/W2031739100","https://openalex.org/W2054662916","https://openalex.org/W2102494751","https://openalex.org/W2156669471","https://openalex.org/W2167940142","https://openalex.org/W4205354563","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644"],"abstract_inverted_index":{"Many":[0],"second":[1,150,215],"order":[2,53,153,190,216,225,274,279],"accurate":[3],"nonoscillatory":[4,154],"schemes":[5,155,217],"are":[6,162],"based":[7,218],"on":[8,219],"the":[9,13,21,47,166,174,189,192,220,252],"minmod":[10,221],"limiter,":[11],"e.g.,":[12],"Nessyahu\u2013Tadmor":[14],"scheme.":[15,280],"It":[16],"is":[17,51,158,186,223],"well":[18],"known":[19,159],"that":[20,188],"<inline-formula":[22,54,79,116,193,228,253],"content-type=\"math/mathml\">":[23,55,80,117,194,229,254],"<mml:math":[24,56,81,118,195,230,255],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[25,57,82,119,196,231,256],"alttext=\"upper":[26,83,197],"L":[27,90,198],"Subscript":[28,91],"p\">":[29],"<mml:semantics>":[30,61,95,126,200,235,260],"<mml:msub>":[31,103,201],"<mml:mi>L</mml:mi>":[32,104,202],"<mml:mi>p</mml:mi>":[33,105,132],"</mml:msub>":[34,106,204],"<mml:annotation":[35,70,110,141,205,244,269],"encoding=\"application/x-tex\">L_p</mml:annotation>":[36],"</mml:semantics>":[37,72,112,145,207,246,271],"</mml:math>":[38,73,113,146,208,247,272],"</inline-formula>":[39,74,114,147,209,248,273],"-error":[40,210],"of":[41,52,176,191,214,224],"monotone":[42,182],"finite":[43],"difference":[44],"methods":[45],"for":[46,75,165,211,275],"linear":[48,178],"advection":[49,168,179],"equation":[50,180],"alttext=\"1":[58,120,257],"slash":[59,233,258],"2\">":[60,199,259],"<mml:mrow>":[62,96,127,236,261],"<mml:mn>1</mml:mn>":[63,99,128,262],"<mml:mrow":[64,238,263],"class=\"MJX-TeXAtom-ORD\">":[65,239,264],"<mml:mo>/</mml:mo>":[66,240,265],"</mml:mrow>":[67,69,109,140,241,243,266,268],"<mml:mn>2</mml:mn>":[68,203,267],"encoding=\"application/x-tex\">1/2</mml:annotation>":[71,270],"initial":[76,183],"data":[77],"in":[78,173,249],"W":[84],"Superscript":[85],"1":[86],"Baseline":[87,93],"left-parenthesis":[88],"upper":[89],"p":[92,122],"right-parenthesis\">":[94],"<mml:msup>":[97],"<mml:mi>W</mml:mi>":[98],"</mml:msup>":[100],"<mml:mo":[101,107],"stretchy=\"false\">(</mml:mo>":[102],"stretchy=\"false\">)</mml:mo>":[108],"encoding=\"application/x-tex\">W^1(L_p)</mml:annotation>":[111],",":[115],"less-than-or-equal-to":[121,123],"normal":[124],"infinity\">":[125],"<mml:mo>":[129,133],"\u2264":[130,134],"</mml:mo>":[131,135],"<mml:mi":[136],"mathvariant=\"normal\">":[137],"\u221e":[138],"</mml:mi>":[139],"encoding=\"application/x-tex\">1\\leq":[142],"p\\leq":[143],"\\infty</mml:annotation>":[144],".":[148],"For":[149],"or":[151],"higher":[152],"very":[156],"little":[157],"because":[160],"they":[161],"nonlinear":[163],"even":[164],"simple":[167],"equation.":[169],"In":[170],"this":[171],"paper,":[172],"case":[175],"a":[177,212],"with":[181],"data,":[184],"it":[185],"shown":[187],"encoding=\"application/x-tex\">L_2</mml:annotation>":[206],"class":[213],"limiter":[222],"at":[226],"least":[227],"alttext=\"5":[232],"8\">":[234],"<mml:mn>5</mml:mn>":[237],"<mml:mn>8</mml:mn>":[242],"encoding=\"application/x-tex\">5/8</mml:annotation>":[245],"contrast":[250],"to":[251],"any":[276],"formally":[277],"first":[278]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-22T06:01:30.510260","created_date":"2025-10-10T00:00:00"}
