{"id":"https://openalex.org/W2790171378","doi":"https://doi.org/10.1090/mcom/3464","title":"Post-processed Galerkin approximation of improved order for wave equations","display_name":"Post-processed Galerkin approximation of improved order for wave equations","publication_year":2019,"publication_date":"2019-06-26","ids":{"openalex":"https://openalex.org/W2790171378","doi":"https://doi.org/10.1090/mcom/3464","mag":"2790171378"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3464","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3464","pdf_url":null,"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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1803.03005","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040109393","display_name":"Markus Bause","orcid":"https://orcid.org/0000-0003-1180-4250"},"institutions":[{"id":"https://openalex.org/I190134885","display_name":"Helmut Schmidt University","ror":"https://ror.org/04e8jbs38","country_code":"DE","type":"education","lineage":["https://openalex.org/I190134885"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"M. Bause","raw_affiliation_strings":["Faculty of Mechanical Engineering, Helmut Schmidt University, Holstenhofweg 85, 22043 Hamburg, Germany","Faculty of Mechanical Engineering Helmut-Schmidt University Holstenhofweg 85 22043 Hamburg Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mechanical Engineering, Helmut Schmidt University, Holstenhofweg 85, 22043 Hamburg, Germany","institution_ids":["https://openalex.org/I190134885"]},{"raw_affiliation_string":"Faculty of Mechanical Engineering Helmut-Schmidt University Holstenhofweg 85 22043 Hamburg Germany","institution_ids":["https://openalex.org/I190134885"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032709485","display_name":"Uwe K\u00f6cher","orcid":"https://orcid.org/0000-0003-3506-121X"},"institutions":[{"id":"https://openalex.org/I190134885","display_name":"Helmut Schmidt University","ror":"https://ror.org/04e8jbs38","country_code":"DE","type":"education","lineage":["https://openalex.org/I190134885"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"U. K\u00f6cher","raw_affiliation_strings":["Faculty of Mechanical Engineering Helmut-Schmidt University Holstenhofweg 85 22043 Hamburg Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mechanical Engineering Helmut-Schmidt University Holstenhofweg 85 22043 Hamburg Germany","institution_ids":["https://openalex.org/I190134885"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101505057","display_name":"Florin A. Radu","orcid":"https://orcid.org/0000-0002-2577-5684"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"F. Radu","raw_affiliation_strings":["Department of Mathematics, University of Bergen, All\u00c3\u00a9gaten 41, 50520 Bergen, Norway","Department of Mathematics, University of Bergen, All\u00e9gaten 41, 50520 Bergen, Norway"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Bergen, All\u00c3\u00a9gaten 41, 50520 Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]},{"raw_affiliation_string":"Department of Mathematics, University of Bergen, All\u00e9gaten 41, 50520 Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006617759","display_name":"Friedhelm Schieweck","orcid":null},"institutions":[{"id":"https://openalex.org/I4210138551","display_name":"University Hospital Magdeburg","ror":"https://ror.org/03m04df46","country_code":"DE","type":"healthcare","lineage":["https://openalex.org/I4210138551"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"F. Schieweck","raw_affiliation_strings":["Faculty of Mathematics, University of Magdeburg, Universit\u00c3\u00a4tsplatz 2, 39106 Magdeburg, Germany","Faculty of Mathematics, University of Magdeburg, Universit\u00e4tsplatz 2, 39106 Magdeburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, University of Magdeburg, Universit\u00c3\u00a4tsplatz 2, 39106 Magdeburg, Germany","institution_ids":["https://openalex.org/I4210138551"]},{"raw_affiliation_string":"Faculty of Mathematics, University of Magdeburg, Universit\u00e4tsplatz 2, 39106 Magdeburg, Germany","institution_ids":["https://openalex.org/I4210138551"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1868,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.45440121,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"89","issue":"322","first_page":"595","last_page":"627"},"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":0.9998000264167786,"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":0.9998000264167786,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9988999962806702,"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/T10514","display_name":"Numerical methods in engineering","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/superconvergence","display_name":"Superconvergence","score":0.7574595212936401},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7498525381088257},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.585829496383667},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.5539733171463013},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5524991750717163},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5483570098876953},{"id":"https://openalex.org/keywords/wave-equation","display_name":"Wave equation","score":0.5346813201904297},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5258657932281494},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.4383399784564972},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4356161653995514},{"id":"https://openalex.org/keywords/time-derivative","display_name":"Time derivative","score":0.43555474281311035},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.42920997738838196},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3950573801994324},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.3940991759300232},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3013809323310852},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27393823862075806}],"concepts":[{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.7574595212936401},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7498525381088257},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.585829496383667},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.5539733171463013},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5524991750717163},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5483570098876953},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.5346813201904297},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5258657932281494},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.4383399784564972},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4356161653995514},{"id":"https://openalex.org/C17685861","wikidata":"https://www.wikidata.org/wiki/Q6960532","display_name":"Time derivative","level":2,"score":0.43555474281311035},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.42920997738838196},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3950573801994324},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.3940991759300232},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3013809323310852},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27393823862075806},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1090/mcom/3464","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3464","pdf_url":null,"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"},{"id":"pmh:oai:arXiv.org:1803.03005","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1803.03005","pdf_url":"https://arxiv.org/pdf/1803.03005","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2790171378","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1803.03005.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1803.03005","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1803.03005","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1803.03005","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1803.03005","pdf_url":"https://arxiv.org/pdf/1803.03005","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"display_name":"Affordable and clean energy","score":0.75,"id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W35607977","https://openalex.org/W1980624993","https://openalex.org/W1981394945","https://openalex.org/W1997909686","https://openalex.org/W2008560581","https://openalex.org/W2022977680","https://openalex.org/W2049794979","https://openalex.org/W2082621526","https://openalex.org/W2087306684","https://openalex.org/W2090050600","https://openalex.org/W2100564583","https://openalex.org/W2145007271","https://openalex.org/W2313566745","https://openalex.org/W2490999188","https://openalex.org/W2540626350","https://openalex.org/W2554356339","https://openalex.org/W2598994884","https://openalex.org/W2615145385","https://openalex.org/W2781230077"],"related_works":["https://openalex.org/W2964283834","https://openalex.org/W2055723554","https://openalex.org/W2900944674","https://openalex.org/W2914281862","https://openalex.org/W1590447734","https://openalex.org/W3034740161","https://openalex.org/W2133147107","https://openalex.org/W2888618297","https://openalex.org/W2322629235","https://openalex.org/W1946642779","https://openalex.org/W2945937089","https://openalex.org/W3161520335","https://openalex.org/W2018233090","https://openalex.org/W2951776525","https://openalex.org/W1976435787","https://openalex.org/W2189522961","https://openalex.org/W2963795298","https://openalex.org/W116626624","https://openalex.org/W2067145579","https://openalex.org/W3157588982"],"abstract_inverted_index":{"We":[0],"introduce":[1],"and":[2],"analyze":[3],"a":[4,24,27,84,103,162,176],"post-processing":[5,15],"for":[6,52,92,115,122,144,183,192],"continuous":[7,25],"variational":[8],"space-time":[9],"discretizations":[10],"of":[11,36,60,70,96,129,135,147,155,161,164,178],"wave":[12,131,196],"problems.":[13],"The":[14,38,120,198],"lifts":[16],"the":[17,34,45,54,73,81,93,97,112,116,127,130,145,159,165,184],"fully":[18],"discrete":[19,74],"approximation":[20,193],"in":[21,40,63,171],"time":[22,41,75,94],"from":[23,140],"to":[26,110,195],"continuously":[28],"differentiable":[29],"one.":[30],"Further,":[31],"it":[32],"increases":[33],"order":[35,62],"convergence.":[37],"discretization":[39],"is":[42,50,77,87,158,169,181,188],"based":[43],"on":[44],"Gauss\u2013Lobatto":[46],"quadrature":[47],"formula":[48],"which":[49,187],"essential":[51,173],"ensuring":[53],"improved":[55],"convergence":[56],"behavior.":[57],"Error":[58],"estimates":[59,91,114,200],"optimal":[61],"various":[64],"norms":[65],"are":[66,100,108,201],"proved.":[67,101],"A":[68,151],"bound":[69],"superconvergence":[71],"at":[72],"nodes":[76],"included.":[78],"To":[79],"show":[80,111],"error":[82,90,113,149,199],"estimates,":[83],"special":[85],"approach":[86,124],"developed.":[88],"First,":[89],"derivative":[95],"post-processed":[98,117,185],"solution":[99,118,137,167,186],"In":[102],"second":[104],"step":[105],"these":[106],"results":[107],"used":[109],"itself.":[119],"need":[121],"this":[123,156],"comes":[125],"through":[126],"structure":[128],"equation.":[132],"Stability":[133],"properties":[134],"its":[136],"preclude":[138],"us":[139],"using":[141],"absorption":[142],"arguments":[143],"control":[146],"certain":[148],"quantities.":[150],"further":[152],"key":[153],"ingredient":[154],"work":[157],"construction":[160],"time-interpolate":[163],"exact":[166],"that":[168],"needed":[170],"an":[172,189],"way.":[174],"Finally,":[175],"conservation":[177],"energy":[179],"property":[180],"shown":[182],"important":[190],"feature":[191],"schemes":[194],"equations.":[197],"confirmed":[202],"by":[203],"numerical":[204],"experiments.":[205]},"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2025-10-10T00:00:00"}
