{"id":"https://openalex.org/W1996560186","doi":"https://doi.org/10.1090/s0025-5718-2012-02663-9","title":"Error estimates for Galerkin approximations of the \u201cclassical\u201d Boussinesq system","display_name":"Error estimates for Galerkin approximations of the \u201cclassical\u201d Boussinesq system","publication_year":2012,"publication_date":"2012-12-12","ids":{"openalex":"https://openalex.org/W1996560186","doi":"https://doi.org/10.1090/s0025-5718-2012-02663-9","mag":"1996560186"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-2012-02663-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2012-02663-9","pdf_url":"https://www.ams.org/mcom/2013-82-282/S0025-5718-2012-02663-9/S0025-5718-2012-02663-9.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/2013-82-282/S0025-5718-2012-02663-9/S0025-5718-2012-02663-9.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109712333","display_name":"Dimitrios Antonopoulos","orcid":null},"institutions":[{"id":"https://openalex.org/I200777214","display_name":"National and Kapodistrian University of Athens","ror":"https://ror.org/04gnjpq42","country_code":"GR","type":"education","lineage":["https://openalex.org/I200777214"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"D. Antonopoulos","raw_affiliation_strings":["Department of Mathematics, University of Athens, 15784 Zographou, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Athens, 15784 Zographou, Greece","institution_ids":["https://openalex.org/I200777214"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004403977","display_name":"V. A. Dougalis","orcid":null},"institutions":[{"id":"https://openalex.org/I200777214","display_name":"National and Kapodistrian University of Athens","ror":"https://ror.org/04gnjpq42","country_code":"GR","type":"education","lineage":["https://openalex.org/I200777214"]},{"id":"https://openalex.org/I4210129470","display_name":"FORTH Institute of Applied and Computational Mathematics","ror":"https://ror.org/02n2yp822","country_code":"GR","type":"facility","lineage":["https://openalex.org/I4210129470","https://openalex.org/I8901234"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"V. Dougalis","raw_affiliation_strings":["Department of Mathematics, University of Athens, 15784 Zographou, Greece \u2013 and \u2013 Institute of Applied and Computational Mathematics, FORTH, 70013 Heraklion, Greece","Department of Mathematics, University of Athens, 15784 Zographou, Greece and Institute of Applied and Computational Mathematics, FORTH, 70013 Heraklion, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Athens, 15784 Zographou, Greece \u2013 and \u2013 Institute of Applied and Computational Mathematics, FORTH, 70013 Heraklion, Greece","institution_ids":["https://openalex.org/I200777214","https://openalex.org/I4210129470"]},{"raw_affiliation_string":"Department of Mathematics, University of Athens, 15784 Zographou, Greece and Institute of Applied and Computational Mathematics, FORTH, 70013 Heraklion, Greece","institution_ids":["https://openalex.org/I200777214"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8334,"has_fulltext":true,"cited_by_count":23,"citation_normalized_percentile":{"value":0.82013253,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"82","issue":"282","first_page":"689","last_page":"717"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.9958000183105469,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9957000017166138,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.846612274646759},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7967617511749268},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.6526336669921875},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.535398542881012},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5347892642021179},{"id":"https://openalex.org/keywords/boussinesq-approximation","display_name":"Boussinesq approximation (buoyancy)","score":0.5338078141212463},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5264019966125488},{"id":"https://openalex.org/keywords/summation-by-parts","display_name":"Summation by parts","score":0.5157440304756165},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.45543110370635986},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.44963452219963074},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.44324690103530884},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.4418644607067108},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.43089932203292847},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39608412981033325},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.34374523162841797},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.07866138219833374},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07380059361457825}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.846612274646759},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7967617511749268},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.6526336669921875},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.535398542881012},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5347892642021179},{"id":"https://openalex.org/C181152433","wikidata":"https://www.wikidata.org/wiki/Q895274","display_name":"Boussinesq approximation (buoyancy)","level":5,"score":0.5338078141212463},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5264019966125488},{"id":"https://openalex.org/C13626590","wikidata":"https://www.wikidata.org/wiki/Q318754","display_name":"Summation by parts","level":2,"score":0.5157440304756165},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.45543110370635986},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.44963452219963074},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.44324690103530884},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.4418644607067108},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.43089932203292847},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39608412981033325},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.34374523162841797},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.07866138219833374},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07380059361457825},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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},{"id":"https://openalex.org/C10899652","wikidata":"https://www.wikidata.org/wiki/Q160329","display_name":"Convection","level":2,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C106836276","wikidata":"https://www.wikidata.org/wiki/Q898249","display_name":"Rayleigh number","level":4,"score":0.0},{"id":"https://openalex.org/C54791560","wikidata":"https://www.wikidata.org/wiki/Q3285020","display_name":"Natural convection","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-2012-02663-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2012-02663-9","pdf_url":"https://www.ams.org/mcom/2013-82-282/S0025-5718-2012-02663-9/S0025-5718-2012-02663-9.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"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-2012-02663-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2012-02663-9","pdf_url":"https://www.ams.org/mcom/2013-82-282/S0025-5718-2012-02663-9/S0025-5718-2012-02663-9.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":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1996560186.pdf","grobid_xml":"https://content.openalex.org/works/W1996560186.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W64052525","https://openalex.org/W305332711","https://openalex.org/W1547305207","https://openalex.org/W1558198389","https://openalex.org/W1595515622","https://openalex.org/W1632757846","https://openalex.org/W1971193413","https://openalex.org/W1977607363","https://openalex.org/W1986788497","https://openalex.org/W1993235715","https://openalex.org/W2011550918","https://openalex.org/W2023341142","https://openalex.org/W2025790909","https://openalex.org/W2028220405","https://openalex.org/W2033104118","https://openalex.org/W2051689409","https://openalex.org/W2074657707","https://openalex.org/W2077464783","https://openalex.org/W2081451815","https://openalex.org/W2082621526","https://openalex.org/W2094865311","https://openalex.org/W2118072606","https://openalex.org/W2137598555","https://openalex.org/W2143167560","https://openalex.org/W2157529765","https://openalex.org/W2314842031","https://openalex.org/W3021722416","https://openalex.org/W4231723373","https://openalex.org/W4242043978"],"related_works":["https://openalex.org/W2055696851","https://openalex.org/W2324487000","https://openalex.org/W4382021736","https://openalex.org/W2120874885","https://openalex.org/W2162026849","https://openalex.org/W2394687667","https://openalex.org/W2040975642","https://openalex.org/W2519394870","https://openalex.org/W2113972433","https://openalex.org/W2893458136"],"abstract_inverted_index":{"We":[0,39],"consider":[1],"the":[2,28,58,84],"\u201cclassical\u201d":[3],"Boussinesq":[4],"system":[5],"in":[6,34,47],"one":[7],"space":[8,48],"dimension":[9],"and":[10,53,62],"its":[11],"symmetric":[12],"analog.":[13],"These":[14],"systems":[15,46],"model":[16],"two-way":[17],"propagation":[18],"of":[19,24,30,78,86],"nonlinear,":[20],"dispersive":[21],"long":[22],"waves":[23],"small":[25],"amplitude":[26],"on":[27],"surface":[29],"an":[31,41],"ideal":[32],"fluid":[33],"a":[35],"uniform":[36],"horizontal":[37],"channel.":[38],"discretize":[40],"initial-boundary-value":[42],"problem":[43],"for":[44,57,64],"these":[45],"using":[49],"Galerkin-finite":[50],"element":[51],"methods":[52],"prove":[54],"error":[55],"estimates":[56],"resulting":[59],"semidiscrete":[60],"problems":[61],"also":[63,91],"their":[65],"fully":[66],"discrete":[67],"analogs":[68],"effected":[69],"by":[70],"explicit":[71],"Runge-Kutta":[72],"time-stepping":[73],"procedures.":[74],"The":[75],"theoretical":[76],"orders":[77],"convergence":[79],"obtained":[80],"are":[81,90],"consistent":[82],"with":[83],"results":[85],"numerical":[87],"experiments":[88],"that":[89],"presented.":[92]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}