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In the idealized setting where time discretization is ignored and the simulation time is large, we provide fully guaranteed upper bounds that are asymptotically constant-free and show that the proposed estimator is efficient and polynomial-degree-robust, meaning that the efficiency constant does not deteriorate as the approximation order is increased. To the best of our knowledge, this work is the first to propose an estimator for the wave equation that is provably reliable and efficient in the same norm. We also explain, without analysis, how the estimator is adapted to cover time discretization by an explicit time integration scheme. Numerical examples illustrate the theory and suggest that it is sharp.<\/jats:p>","DOI":"10.1137\/22m1485619","type":"journal-article","created":{"date-parts":[[2023,7,10]],"date-time":"2023-07-10T10:33:01Z","timestamp":1688985181000},"page":"A1591-A1620","source":"Crossref","is-referenced-by-count":8,"title":["Asymptotically Constant-Free and Polynomial-Degree-Robust a Posteriori Estimates for Space Discretizations of the Wave Equation"],"prefix":"10.1137","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6210-0774","authenticated-orcid":true,"given":"T.","family":"Chaumont-Frelet","sequence":"first","affiliation":[{"name":"Universit\u00e9 C\u00f4te d\u2019Azur, Inria, CNRS, LJAD, 2004 Route des Lucioles, 06902 Valbonne, France."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,7,10]]},"reference":[{"key":"ref1","volume-title":"Sobolev Spaces","author":"Adams R.","year":"2003"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(02)00400-0"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2005.08.003"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1002\/9781118032824"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-011-0363-6"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(99)00242-X"},{"key":"ref7","first-page":"5","volume":"10","author":"Arcangeli R.","year":"1976","journal-title":"Anal. 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