{"id":"https://openalex.org/W2890749070","doi":"https://doi.org/10.1515/cmam-2018-0032","title":"A Priori Error Analysis of a Discontinuous Galerkin Scheme for the Magnetic Induction Equation","display_name":"A Priori Error Analysis of a Discontinuous Galerkin Scheme for the Magnetic Induction Equation","publication_year":2018,"publication_date":"2018-09-11","ids":{"openalex":"https://openalex.org/W2890749070","doi":"https://doi.org/10.1515/cmam-2018-0032","mag":"2890749070"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2018-0032","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2018-0032","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","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/A5080222191","display_name":"Tanmay Sarkar","orcid":"https://orcid.org/0000-0001-8565-9864"},"institutions":[{"id":"https://openalex.org/I4210127441","display_name":"Indian Institute of Technology Jammu","ror":"https://ror.org/02f0vsw63","country_code":"IN","type":"education","lineage":["https://openalex.org/I4210127441"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Tanmay Sarkar","raw_affiliation_strings":["Tata Instiute of Fundamental Research , Centre for Applicable Mathematics , Post Bag No. 6503, GKVK Post Office, Sharada Nagar, Chikkabommasandra , Bangalore 560065 ; and Department of Mathematics, Indian Institute of Technology Jammu, NH-44 Bypass Road, Jagti, Jammu 181 221 , India","Department of Mathematics, Indian Institute of Technology Jammu, NH-44 Bypass Road, Jagti, Jammu 181 221, India"],"affiliations":[{"raw_affiliation_string":"Tata Instiute of Fundamental Research , Centre for Applicable Mathematics , Post Bag No. 6503, GKVK Post Office, Sharada Nagar, Chikkabommasandra , Bangalore 560065 ; and Department of Mathematics, Indian Institute of Technology Jammu, NH-44 Bypass Road, Jagti, Jammu 181 221 , India","institution_ids":["https://openalex.org/I4210127441"]},{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology Jammu, NH-44 Bypass Road, Jagti, Jammu 181 221, India","institution_ids":["https://openalex.org/I4210127441"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5080222191"],"corresponding_institution_ids":["https://openalex.org/I4210127441"],"apc_list":null,"apc_paid":null,"fwci":0.2027,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.50693218,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"20","issue":"1","first_page":"121","last_page":"140"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998999834060669,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998999834060669,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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":0.9987000226974487,"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/piecewise","display_name":"Piecewise","score":0.5757312774658203},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5531948804855347},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.492343544960022},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4782611131668091},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4678797125816345},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.43185630440711975},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38050761818885803},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.32134291529655457}],"concepts":[{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5757312774658203},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5531948804855347},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.492343544960022},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4782611131668091},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4678797125816345},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.43185630440711975},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38050761818885803},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.32134291529655457},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/cmam-2018-0032","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2018-0032","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W140909251","https://openalex.org/W628726389","https://openalex.org/W1509923322","https://openalex.org/W1538356049","https://openalex.org/W1969647398","https://openalex.org/W1994841670","https://openalex.org/W1996082552","https://openalex.org/W1999105805","https://openalex.org/W2014282047","https://openalex.org/W2034154296","https://openalex.org/W2041523977","https://openalex.org/W2042388195","https://openalex.org/W2043140788","https://openalex.org/W2065785823","https://openalex.org/W2073263351","https://openalex.org/W2081377160","https://openalex.org/W2085961649","https://openalex.org/W2104039162","https://openalex.org/W2104949606","https://openalex.org/W2116093909","https://openalex.org/W2141169977","https://openalex.org/W2423973828","https://openalex.org/W2743672113","https://openalex.org/W3021722416","https://openalex.org/W3103185977","https://openalex.org/W4210300254","https://openalex.org/W4233665781"],"related_works":["https://openalex.org/W1978042415","https://openalex.org/W2133255715","https://openalex.org/W2066091055","https://openalex.org/W2040186499","https://openalex.org/W2016360082","https://openalex.org/W4232993046","https://openalex.org/W4377003522","https://openalex.org/W2045613449","https://openalex.org/W85224956","https://openalex.org/W2046313492"],"abstract_inverted_index":{"Abstract":[0],"We":[1,103],"perform":[2],"the":[3,13,20,34,90,95,105,146],"error":[4,106],"analysis":[5],"of":[6],"a":[7,46],"stabilized":[8],"discontinuous":[9,26],"Galerkin":[10],"scheme":[11,99],"for":[12,41,100,122,129],"initial":[14],"boundary":[15],"value":[16],"problem":[17],"associated":[18],"with":[19,132],"magnetic":[21],"induction":[22],"equations":[23],"using":[24],"standard":[25,147],"Lagrange":[27],"basis":[28],"functions.":[29],"In":[30],"order":[31],"to":[32],"obtain":[33,119],"quasi-optimal":[35,120],"convergence":[36,121],"incorporating":[37],"second-order":[38],"Runge\u2013Kutta":[39,98],"schemes":[40],"time":[42,101,128],"discretization,":[43],"we":[44,93],"need":[45],"strengthened":[47],"<m:math":[48,60,109,135],"xmlns:m=\"http://www.w3.org/1998/Math/MathML\">":[49,61,110,136],"<m:mrow>":[50,62,63,72,137],"<m:mn>4</m:mn>":[51,73],"<m:mo>/</m:mo>":[52,74],"<m:mn>3</m:mn>":[53,75],"</m:mrow>":[54,68,76,78,141],"</m:math>":[55,79,115,142],"{4/3}":[56],"-CFL":[57],"condition":[58],"(":[59],"<m:mi":[64],"mathvariant=\"normal\">\u0394</m:mi>":[65],"<m:mo>\u2062</m:mo>":[66],"<m:mi>t</m:mi>":[67],"<m:mo>\u223c</m:mo>":[69],"<m:msup>":[70,111],"<m:mi>h</m:mi>":[71],"</m:msup>":[77,114],"{\\Delta":[80],"t\\sim":[81],"h^{4/3}}":[82],").":[83],"To":[84],"overcome":[85],"this":[86],"unusual":[87],"restriction":[88],"on":[89],"CFL":[91,148],"condition,":[92],"consider":[94],"explicit":[96],"third-order":[97],"discretization.":[102],"demonstrate":[104],"estimates":[107],"in":[108,125],"<m:mi>L</m:mi>":[112],"<m:mn>2</m:mn>":[113],"{L^{2}}":[116],"-sense":[117],"and":[118,127],"smooth":[123],"solution":[124],"space":[126],"piecewise":[130],"polynomials":[131],"any":[133],"degree":[134],"<m:mi>l</m:mi>":[138],"<m:mo>\u2265</m:mo>":[139],"<m:mn>1</m:mn>":[140],"{l\\geq":[143],"1}":[144],"under":[145],"condition.":[149]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}