{"id":"https://openalex.org/W2015829426","doi":"https://doi.org/10.1090/s0025-5718-98-00946-6","title":"A space-time finite element method for the nonlinear Schr\u00f6dinger equation: the discontinuous Galerkin method","display_name":"A space-time finite element method for the nonlinear Schr\u00f6dinger equation: the discontinuous Galerkin method","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W2015829426","doi":"https://doi.org/10.1090/s0025-5718-98-00946-6","mag":"2015829426"},"language":"lv","primary_location":{"id":"doi:10.1090/s0025-5718-98-00946-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-98-00946-6","pdf_url":"https://www.ams.org/mcom/1998-67-222/S0025-5718-98-00946-6/S0025-5718-98-00946-6.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":null,"license_id":null,"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":"bronze","oa_url":"https://www.ams.org/mcom/1998-67-222/S0025-5718-98-00946-6/S0025-5718-98-00946-6.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039118559","display_name":"Ohannes A. Karakashian","orcid":"https://orcid.org/0000-0001-8309-8450"},"institutions":[{"id":"https://openalex.org/I75027704","display_name":"University of Tennessee at Knoxville","ror":"https://ror.org/020f3ap87","country_code":"US","type":"education","lineage":["https://openalex.org/I75027704"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ohannes Karakashian","raw_affiliation_strings":["Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37966"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37966","institution_ids":["https://openalex.org/I75027704"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5105693474","display_name":"Charalambos Makridakis","orcid":null},"institutions":[{"id":"https://openalex.org/I142617266","display_name":"University of Crete","ror":"https://ror.org/00dr28g20","country_code":"GR","type":"education","lineage":["https://openalex.org/I142617266"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Charalambos Makridakis","raw_affiliation_strings":["Department of Mathematics, University of Crete, 714 09 Heraklion, Crete, Greece","Department of Mathematics, University of Crete, 714 09, Heraklion, Crete, Greece"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Crete, 714 09 Heraklion, Crete, Greece","institution_ids":["https://openalex.org/I142617266"]},{"raw_affiliation_string":"Department of Mathematics, University of Crete, 714 09, Heraklion, Crete, Greece","institution_ids":["https://openalex.org/I142617266"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5039118559"],"corresponding_institution_ids":["https://openalex.org/I75027704"],"apc_list":null,"apc_paid":null,"fwci":1.8628,"has_fulltext":true,"cited_by_count":152,"citation_normalized_percentile":{"value":0.85569732,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"67","issue":"222","first_page":"479","last_page":"499"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9994999766349792,"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":0.9994999766349792,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9987999796867371,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9976000189781189,"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/algorithm","display_name":"Algorithm","score":0.5686776041984558},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5130206942558289}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5686776041984558},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5130206942558289}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-98-00946-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-98-00946-6","pdf_url":"https://www.ams.org/mcom/1998-67-222/S0025-5718-98-00946-6/S0025-5718-98-00946-6.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":null,"license_id":null,"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/s0025-5718-98-00946-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-98-00946-6","pdf_url":"https://www.ams.org/mcom/1998-67-222/S0025-5718-98-00946-6/S0025-5718-98-00946-6.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":null,"license_id":null,"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/G2142905773","display_name":"U.S.-Greece Cooperative Research:  Numerical Studies of     Nonlinear, Dispersive Wave Equations","funder_award_id":"9504845","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"},{"id":"https://openalex.org/F4320322644","display_name":"University of Crete","ror":"https://ror.org/00dr28g20"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2015829426.pdf","grobid_xml":"https://content.openalex.org/works/W2015829426.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W202835528","https://openalex.org/W1492326914","https://openalex.org/W1510817630","https://openalex.org/W1565460255","https://openalex.org/W1970850839","https://openalex.org/W1979146918","https://openalex.org/W1985787639","https://openalex.org/W1986788497","https://openalex.org/W1987196790","https://openalex.org/W1989819667","https://openalex.org/W1995504856","https://openalex.org/W1997909686","https://openalex.org/W2000382398","https://openalex.org/W2021049593","https://openalex.org/W2033099995","https://openalex.org/W2038191139","https://openalex.org/W2038626747","https://openalex.org/W2041523977","https://openalex.org/W2050330601","https://openalex.org/W2055893851","https://openalex.org/W2066944044","https://openalex.org/W2073732659","https://openalex.org/W2079138830","https://openalex.org/W2082621526","https://openalex.org/W2088552913","https://openalex.org/W2218004560","https://openalex.org/W2429258439","https://openalex.org/W2508983562","https://openalex.org/W2991313792","https://openalex.org/W4211036616","https://openalex.org/W4231297994","https://openalex.org/W4241341410","https://openalex.org/W4250831033","https://openalex.org/W4291439952","https://openalex.org/W4292166829","https://openalex.org/W4293515545","https://openalex.org/W4302394292","https://openalex.org/W4327726860","https://openalex.org/W6688492276"],"related_works":["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","https://openalex.org/W2142036596"],"abstract_inverted_index":{"The":[0],"convergence":[1],"of":[2,22],"the":[3,8,20,23,90],"discontinuous":[4],"Galerkin":[5],"method":[6],"for":[7],"nonlinear":[9],"(cubic)":[10],"Schr\u00f6dinger":[11],"equation":[12],"is":[13],"analyzed":[14],"in":[15,32],"this":[16],"paper.":[17],"We":[18],"show":[19],"existence":[21],"resulting":[24],"approximations":[25],"and":[26],"prove":[27],"optimal":[28],"order":[29],"error":[30],"estimates":[31,83],"<inline-formula":[33],"content-type=\"math/mathml\">":[34],"<mml:math":[35],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[36],"alttext=\"upper":[37],"L":[38,45],"Superscript":[39],"normal":[40],"infinity":[41],"Baseline":[42],"left-parenthesis":[43],"upper":[44],"squared":[46],"right-parenthesis":[47],"period\">":[48],"<mml:semantics>":[49],"<mml:mrow>":[50],"<mml:msup>":[51,63],"<mml:mi>L</mml:mi>":[52,64],"<mml:mrow":[53,65],"class=\"MJX-TeXAtom-ORD\">":[54,66],"<mml:mi":[55],"mathvariant=\"normal\">":[56],"\u221e":[57],"</mml:mi>":[58],"</mml:mrow>":[59,68,73],"</mml:msup>":[60,69],"<mml:mo":[61,70],"stretchy=\"false\">(</mml:mo>":[62],"<mml:mn>2</mml:mn>":[67],"stretchy=\"false\">)</mml:mo>":[71],"<mml:mo>.</mml:mo>":[72],"<mml:annotation":[74],"encoding=\"application/x-tex\">L^{\\infty":[75],"}(L^{2}":[76],")":[77],".</mml:annotation>":[78],"</mml:semantics>":[79],"</mml:math>":[80],"</inline-formula>":[81],"These":[82],"are":[84],"valid":[85],"under":[86],"weak":[87],"restrictions":[88],"on":[89],"space-time":[91],"mesh.":[92]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":17},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":11},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}
