{"id":"https://openalex.org/W2028948360","doi":"https://doi.org/10.1090/s0025-5718-07-02015-7","title":"Uniform error estimates in the finite element method for a singularly perturbed reaction-diffusion problem","display_name":"Uniform error estimates in the finite element method for a singularly perturbed reaction-diffusion problem","publication_year":2007,"publication_date":"2007-05-14","ids":{"openalex":"https://openalex.org/W2028948360","doi":"https://doi.org/10.1090/s0025-5718-07-02015-7","mag":"2028948360"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-07-02015-7","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-07-02015-7","pdf_url":"https://www.ams.org/mcom/2008-77-261/S0025-5718-07-02015-7/S0025-5718-07-02015-7.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/2008-77-261/S0025-5718-07-02015-7/S0025-5718-07-02015-7.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016780750","display_name":"Dmitriy Leykekhman","orcid":"https://orcid.org/0000-0001-9643-5540"},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Dmitriy Leykekhman","raw_affiliation_strings":["Department of Computational and Applied Mathematics, Rice University, Houston, Texas 77005","Department of Computational and Applied Mathematics Rice University Houston Texas 77005"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computational and Applied Mathematics, Rice University, Houston, Texas 77005","institution_ids":["https://openalex.org/I74775410"]},{"raw_affiliation_string":"Department of Computational and Applied Mathematics Rice University Houston Texas 77005","institution_ids":["https://openalex.org/I74775410"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5016780750"],"corresponding_institution_ids":["https://openalex.org/I74775410"],"apc_list":null,"apc_paid":null,"fwci":0.5085,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.66324148,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"77","issue":"261","first_page":"21","last_page":"39"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":1.0,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":1.0,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9991999864578247,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9965999722480774,"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":0.886000394821167},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6617742776870728},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.6546165943145752},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.6407660245895386},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.639491617679596},{"id":"https://openalex.org/keywords/reaction\u2013diffusion-system","display_name":"Reaction\u2013diffusion system","score":0.6393143534660339},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5756646394729614},{"id":"https://openalex.org/keywords/neumann-boundary-condition","display_name":"Neumann boundary condition","score":0.49959492683410645},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.47533726692199707},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.4546606242656708},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.4427946209907532},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.44066670536994934},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4278530478477478},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.27049922943115234},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05843892693519592}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.886000394821167},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6617742776870728},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.6546165943145752},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.6407660245895386},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.639491617679596},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.6393143534660339},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5756646394729614},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.49959492683410645},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.47533726692199707},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.4546606242656708},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.4427946209907532},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.44066670536994934},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4278530478477478},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.27049922943115234},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05843892693519592},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","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},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/s0025-5718-07-02015-7","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-07-02015-7","pdf_url":"https://www.ams.org/mcom/2008-77-261/S0025-5718-07-02015-7/S0025-5718-07-02015-7.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:10.1.1.153.8786","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.153.8786","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/2008-77-261/S0025-5718-07-02015-7/S0025-5718-07-02015-7.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.567.9859","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.567.9859","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uconn.edu/~leykekhman/my_papers/perturbed_intro5.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-07-02015-7","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-07-02015-7","pdf_url":"https://www.ams.org/mcom/2008-77-261/S0025-5718-07-02015-7/S0025-5718-07-02015-7.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":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2028948360.pdf","grobid_xml":"https://content.openalex.org/works/W2028948360.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W94976795","https://openalex.org/W1602435288","https://openalex.org/W1608340114","https://openalex.org/W1955535265","https://openalex.org/W1989819667","https://openalex.org/W2005171998","https://openalex.org/W2007751122","https://openalex.org/W2007962250","https://openalex.org/W2023868969","https://openalex.org/W2060713120","https://openalex.org/W2066335031","https://openalex.org/W4233226319","https://openalex.org/W4248116268"],"related_works":["https://openalex.org/W3013085049","https://openalex.org/W1560496689","https://openalex.org/W4386900933","https://openalex.org/W4385301946","https://openalex.org/W2124287120","https://openalex.org/W4297797135","https://openalex.org/W2320356300","https://openalex.org/W2000865352","https://openalex.org/W2382294907","https://openalex.org/W2774510546"],"abstract_inverted_index":{"Consider":[0],"the":[1,143,170],"problem":[2],"<inline-formula":[3,57,86,130,150,177,190,214,233],"content-type=\"math/mathml\">":[4,58,87,131,151,178,191,215,234],"<mml:math":[5,59,88,132,152,179,192,216,235],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[6,60,89,133,153,180,193,217,236],"alttext=\"minus":[7],"epsilon":[8,92],"squared":[9],"normal":[10],"upper":[11,62,65],"Delta":[12],"u":[13,15],"plus":[14],"equals":[16],"f\">":[17],"<mml:semantics>":[18,67,95,135,155,182,195,219,238],"<mml:mrow>":[19,96],"<mml:mo>":[20,102],"\u2212":[21],"</mml:mo>":[22,104],"<mml:msup>":[23,68],"<mml:mi>":[24,99,156,196,239],"\u03f5":[25,100,157,197,240],"</mml:mi>":[26,32,101,158,198,241],"<mml:mn>2</mml:mn>":[27],"</mml:msup>":[28,75],"<mml:mi":[29,71],"mathvariant=\"normal\">":[30],"\u0394":[31],"<mml:mi>u</mml:mi>":[33,35],"<mml:mo>+</mml:mo>":[34],"<mml:mo>=</mml:mo>":[36],"<mml:mi>f</mml:mi>":[37],"</mml:mrow>":[38,73,106],"<mml:annotation":[39,76,107,137,159,184,199,221,242],"encoding=\"application/x-tex\">-\\epsilon":[40],"^2\\Delta":[41],"u+u=f</mml:annotation>":[42],"</mml:semantics>":[43,79,111,139,161,186,201,223,244],"</mml:math>":[44,80,112,140,162,187,202,224,245],"</inline-formula>":[45,81,113,141,163,188,203,225,246],"with":[46,230],"homogeneous":[47],"Neumann":[48],"boundary":[49],"condition":[50],"in":[51,56,213],"a":[52,124],"bounded":[53],"smooth":[54],"domain":[55],"alttext=\"double-struck":[61],"R":[63],"Superscript":[64],"N\">":[66],"<mml:mrow":[69],"class=\"MJX-TeXAtom-ORD\">":[70],"mathvariant=\"double-struck\">R</mml:mi>":[72],"<mml:mi>N</mml:mi>":[74],"encoding=\"application/x-tex\">\\mathbb":[77],"{R}^N</mml:annotation>":[78],".":[82,164],"The":[83,116],"whole":[84],"range":[85],"alttext=\"0":[90],"greater-than":[91],"less-than-or-equal-to":[93],"1\">":[94],"<mml:mn>0</mml:mn>":[97],"<mml:mo>&gt;</mml:mo>":[98],"\u2264":[103],"<mml:mn>1</mml:mn>":[105],"encoding=\"application/x-tex\">0&gt;\\epsilon":[108],"\\le":[109],"1</mml:annotation>":[110],"is":[114,121,145,204],"treated.":[115],"Galerkin":[117],"finite":[118],"element":[119],"method":[120],"used":[122],"on":[123,176],"globally":[125],"quasi-uniform":[126],"mesh":[127,144],"of":[128,149,168],"size":[129],"alttext=\"h\">":[134,181,218],"<mml:mi>h</mml:mi>":[136,183,220],"encoding=\"application/x-tex\">h</mml:annotation>":[138,185,222],";":[142],"fixed":[146],"and":[147,189],"independent":[148],"alttext=\"epsilon\">":[154,194,237],"encoding=\"application/x-tex\">\\epsilon</mml:annotation>":[160,200,243],"A":[165],"precise":[166],"analysis":[167],"how":[169],"error":[171,211],"at":[172],"each":[173],"point":[174],"depends":[175],"presented.":[205],"As":[206],"an":[207],"application,":[208],"first":[209],"order":[210],"estimates":[212],",":[226,247],"which":[227],"are":[228,248],"uniform":[229],"respect":[231],"to":[232],"given.":[249]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}