{"id":"https://openalex.org/W7125830016","doi":"https://doi.org/10.1007/s10444-026-10282-y","title":"Stable least-squares space-time boundary element methods for the wave equation","display_name":"Stable least-squares space-time boundary element methods for the wave equation","publication_year":2026,"publication_date":"2026-01-27","ids":{"openalex":"https://openalex.org/W7125830016","doi":"https://doi.org/10.1007/s10444-026-10282-y"},"language":"en","primary_location":{"id":"doi:10.1007/s10444-026-10282-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10444-026-10282-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10444-026-10282-y.pdf","source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10444-026-10282-y.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5123966127","display_name":"Daniel Hoonhout","orcid":null},"institutions":[{"id":"https://openalex.org/I4210093035","display_name":"Materials innovation institute","ror":"https://ror.org/00fyemf28","country_code":"NL","type":"facility","lineage":["https://openalex.org/I4210093035"]},{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Daniel Hoonhout","raw_affiliation_strings":["Delft Institute of Applied Mathematics, TU Delft, Mekelweg 4, 2628 CD, Delft, The Netherlands"],"raw_orcid":"https://orcid.org/0009-0002-0994-6524","affiliations":[{"raw_affiliation_string":"Delft Institute of Applied Mathematics, TU Delft, Mekelweg 4, 2628 CD, Delft, The Netherlands","institution_ids":["https://openalex.org/I98358874","https://openalex.org/I4210093035"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046290186","display_name":"Richard L\u00f6scher","orcid":null},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Richard L\u00f6scher","raw_affiliation_strings":["Institut f\u00fcr Angewandte Mathematik, TU Graz, Steyrergasse 30, 8010, Graz, Austria"],"raw_orcid":"https://orcid.org/0000-0002-6155-1178","affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Angewandte Mathematik, TU Graz, Steyrergasse 30, 8010, Graz, Austria","institution_ids":["https://openalex.org/I4092182"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037762950","display_name":"Olaf Steinbach","orcid":"https://orcid.org/0000-0002-2552-3022"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Olaf Steinbach","raw_affiliation_strings":["Institut f\u00fcr Angewandte Mathematik, TU Graz, Steyrergasse 30, 8010, Graz, Austria"],"raw_orcid":"https://orcid.org/0000-0002-2552-3022","affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Angewandte Mathematik, TU Graz, Steyrergasse 30, 8010, Graz, Austria","institution_ids":["https://openalex.org/I4092182"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5123950948","display_name":"Carolina Urz\u00faa\u2013Torres","orcid":null},"institutions":[{"id":"https://openalex.org/I4210093035","display_name":"Materials innovation institute","ror":"https://ror.org/00fyemf28","country_code":"NL","type":"facility","lineage":["https://openalex.org/I4210093035"]},{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Carolina Urz\u00faa\u2013Torres","raw_affiliation_strings":["Delft Institute of Applied Mathematics, TU Delft, Mekelweg 4, 2628 CD, Delft, The Netherlands"],"raw_orcid":"https://orcid.org/0000-0003-0055-6175","affiliations":[{"raw_affiliation_string":"Delft Institute of Applied Mathematics, TU Delft, Mekelweg 4, 2628 CD, Delft, The Netherlands","institution_ids":["https://openalex.org/I98358874","https://openalex.org/I4210093035"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5037762950"],"corresponding_institution_ids":["https://openalex.org/I4092182"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.1655487,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"52","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.44449999928474426,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.44449999928474426,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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":0.18729999661445618,"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"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.06849999725818634,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/boundary-element-method","display_name":"Boundary element method","score":0.5659000277519226},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5382000207901001},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.5152000188827515},{"id":"https://openalex.org/keywords/boundary-knot-method","display_name":"Boundary knot method","score":0.5127000212669373},{"id":"https://openalex.org/keywords/mixed-boundary-condition","display_name":"Mixed boundary condition","score":0.4984000027179718},{"id":"https://openalex.org/keywords/singular-boundary-method","display_name":"Singular boundary method","score":0.4952999949455261},{"id":"https://openalex.org/keywords/free-boundary-problem","display_name":"Free boundary problem","score":0.4927999973297119},{"id":"https://openalex.org/keywords/robin-boundary-condition","display_name":"Robin boundary condition","score":0.4876999855041504},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.44510000944137573}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8216000199317932},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.685699999332428},{"id":"https://openalex.org/C63632240","wikidata":"https://www.wikidata.org/wiki/Q1935004","display_name":"Boundary element method","level":3,"score":0.5659000277519226},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5382000207901001},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.5152000188827515},{"id":"https://openalex.org/C52890695","wikidata":"https://www.wikidata.org/wiki/Q4949966","display_name":"Boundary knot method","level":4,"score":0.5127000212669373},{"id":"https://openalex.org/C42045870","wikidata":"https://www.wikidata.org/wiki/Q2992268","display_name":"Mixed boundary condition","level":3,"score":0.4984000027179718},{"id":"https://openalex.org/C82047721","wikidata":"https://www.wikidata.org/wiki/Q7524247","display_name":"Singular boundary method","level":4,"score":0.4952999949455261},{"id":"https://openalex.org/C154416045","wikidata":"https://www.wikidata.org/wiki/Q5500196","display_name":"Free boundary problem","level":3,"score":0.4927999973297119},{"id":"https://openalex.org/C108257041","wikidata":"https://www.wikidata.org/wiki/Q748993","display_name":"Robin boundary condition","level":4,"score":0.4876999855041504},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.44510000944137573},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.4260999858379364},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.423799991607666},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4198000133037567},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4004000127315521},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.3815999925136566},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.38019999861717224},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.3799999952316284},{"id":"https://openalex.org/C8828549","wikidata":"https://www.wikidata.org/wiki/Q837924","display_name":"Bilinear form","level":2,"score":0.36640000343322754},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.3529999852180481},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.35269999504089355},{"id":"https://openalex.org/C65826597","wikidata":"https://www.wikidata.org/wiki/Q17099589","display_name":"Poincar\u00e9\u2013Steklov operator","level":5,"score":0.35249999165534973},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.3382999897003174},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.31049999594688416},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.28130000829696655},{"id":"https://openalex.org/C48395688","wikidata":"https://www.wikidata.org/wiki/Q6823714","display_name":"Method of fundamental solutions","level":5,"score":0.2678999900817871},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.25769999623298645}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10444-026-10282-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10444-026-10282-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10444-026-10282-y.pdf","source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s10444-026-10282-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10444-026-10282-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10444-026-10282-y.pdf","source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310430","display_name":"TU Graz, Internationale Beziehungen und Mobilit\u00e4tsprogramme","ror":"https://ror.org/00d7xrm67"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7125830016.pdf","grobid_xml":"https://content.openalex.org/works/W7125830016.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W1549879090","https://openalex.org/W1555557982","https://openalex.org/W1976385614","https://openalex.org/W1994177753","https://openalex.org/W2006697861","https://openalex.org/W2039924562","https://openalex.org/W2063288147","https://openalex.org/W2075350180","https://openalex.org/W2093117377","https://openalex.org/W2134350470","https://openalex.org/W2135450684","https://openalex.org/W2135764443","https://openalex.org/W2170987671","https://openalex.org/W2284025117","https://openalex.org/W2305495190","https://openalex.org/W2313566745","https://openalex.org/W2461259506","https://openalex.org/W2494040823","https://openalex.org/W2496081756","https://openalex.org/W2539349066","https://openalex.org/W2545270568","https://openalex.org/W2559827045","https://openalex.org/W2594128612","https://openalex.org/W2602232473","https://openalex.org/W2694859881","https://openalex.org/W2734915834","https://openalex.org/W2898723628","https://openalex.org/W2913877309","https://openalex.org/W2976250660","https://openalex.org/W3014898465","https://openalex.org/W3047205608","https://openalex.org/W3135013903","https://openalex.org/W3151049333","https://openalex.org/W3156968244","https://openalex.org/W3159995363","https://openalex.org/W3167222941","https://openalex.org/W3175552985","https://openalex.org/W3177388523","https://openalex.org/W4229840132","https://openalex.org/W4244627485","https://openalex.org/W4255871072","https://openalex.org/W4408283201","https://openalex.org/W7117154069"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper,":[3],"we":[4,153],"recast":[5],"the":[6,11,26,75,79,104,127,132,145,156,176,179,189],"variational":[7],"formulation":[8,129,158],"corresponding":[9],"to":[10,181],"single":[12],"layer":[13],"boundary":[14,77,123,184],"integral":[15,185],"operator":[16],"$$\\varvec{{\\text":[17],"{\\textsf{V}}}}$$":[18],"<mml:math":[19,36,58,86],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[20,37,59,87],"<mml:mrow>":[21,38,43,60,88],"<mml:mtext>V</mml:mtext>":[22],"</mml:mrow>":[23,47,48,72,99],"</mml:math>":[24,49,73,100],"for":[25,126,168],"wave":[27],"equation":[28],"as":[29,109],"a":[30,110,160],"minimization":[31,105],"problem":[32,106],"in":[33,188],"$$\\varvec{L^2(\\Sigma":[34],")}$$":[35],"<mml:msup>":[39],"<mml:mi>L</mml:mi>":[40],"<mml:mn>2</mml:mn>":[41],"</mml:msup>":[42],"<mml:mo>(</mml:mo>":[44,67,94],"<mml:mi>\u03a3</mml:mi>":[45,61],"<mml:mo>)</mml:mo>":[46,71,98],",":[50],"where":[51],"$$\\varvec{\\Sigma":[52],":=":[53],"\\partial":[54],"\\Omega":[55,83],"\\times":[56,84],"(0,T)}$$":[57,85],"<mml:mo>:</mml:mo>":[62,90],"<mml:mo>=</mml:mo>":[63,91],"<mml:mi>\u2202</mml:mi>":[64],"<mml:mi>\u03a9</mml:mi>":[65,92],"<mml:mo>\u00d7</mml:mo>":[66,93],"<mml:mn>0</mml:mn>":[68,95],"<mml:mo>,</mml:mo>":[69,96],"<mml:mi>T</mml:mi>":[70,97],"is":[74,107,117,136,149],"lateral":[76],"of":[78,178],"space-time":[80],"domain":[81],"$$\\varvec{Q:=":[82],"<mml:mi>Q</mml:mi>":[89],".":[101],"For":[102],"discretization,":[103],"restated":[108],"mixed":[111,128,157],"saddle":[112],"point":[113],"formulation.":[114],"Unique":[115],"solvability":[116],"established":[118],"by":[119],"combining":[120],"conforming":[121],"nested":[122],"element":[124],"spaces":[125],"such":[130],"that":[131,155],"related":[133],"bilinear":[134],"form":[135],"discrete":[137,146],"inf-sup":[138,147],"stable.":[139],"We":[140,170],"analyze":[141],"under":[142],"which":[143,164],"conditions":[144],"stability":[148],"satisfied,":[150],"and":[151],"moreover,":[152],"show":[154],"provides":[159],"simple":[161],"error":[162],"indicator,":[163],"can":[165],"be":[166],"used":[167,187],"adaptivity.":[169],"present":[171],"several":[172],"numerical":[173],"experiments":[174],"showing":[175],"applicability":[177],"method":[180],"different":[182],"time-domain":[183],"formulations":[186],"literature.":[190]},"counts_by_year":[],"updated_date":"2026-05-05T08:41:31.759640","created_date":"2026-01-28T00:00:00"}