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We discuss the algorithmic challenges and investigate the proposed method in numerical experiments. In particular, we study the performance and improved convergence rates with respect to the energy norm for problems dominated by spatial, temporal,\u00a0or traveling singularities of the solution. The efficiency of the considered rigorous and heuristic a posteriori error indicators is discussed.<\/jats:p>","DOI":"10.1137\/25m1782170","type":"journal-article","created":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T09:00:17Z","timestamp":1776070817000},"page":"A984-A1005","source":"Crossref","is-referenced-by-count":0,"title":["A Space-Time Adaptive Boundary Element Method for the Wave Equation"],"prefix":"10.1137","volume":"48","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4699-4261","authenticated-orcid":true,"given":"A.","family":"Aimi","sequence":"first","affiliation":[{"name":"University of Parma, Member of the INdAM-GNCS Research Group, 43121 Parma PR, Italy."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5339-0709","authenticated-orcid":true,"given":"G.","family":"Di Credico","sequence":"additional","affiliation":[{"name":"University of Parma, Member of the INdAM-GNCS Research Group, 43121 Parma PR, Italy."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"H.","family":"Gimperlein","sequence":"additional","affiliation":[{"name":"University of Innsbruck, 6020 Innsbruck, Austria."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7054-8579","authenticated-orcid":true,"given":"C.","family":"Guardasoni","sequence":"additional","affiliation":[{"name":"University of Parma, Member of the INdAM-GNCS Research Group, 43121 Parma PR, Italy."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2026,4,13]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2022.05.024"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2023.116296"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2025.08.020"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-023-01355-x"},{"key":"ref5","first-page":"147","volume":"2","author":"Aimi A.","year":"2011","journal-title":"Rivista Matematica dell\u2019Universit\u00e0 di Parma"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1002\/nme.2660"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1002\/mma.1670080127"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-031-13220-9"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2019.124726"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492924000011"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1137\/22M1485619"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/2025027"},{"key":"ref13","unstructured":"L. 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