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Our method extends the scheme of French and Peterson (1996), incorporating exponential weights in time, which yield an inf\u2013sup stability condition for arbitrary choices of discrete subspaces, including spline spaces, without restrictions on the mesh size or time step. Moreover, using elliptic projections, we derive optimal convergence rates in both the energy and\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$L^2$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:msup>\n                            <mml:mi>L<\/mml:mi>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:msup>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    norms for sufficiently smooth solutions and for any choice of space\u2013time tensor product subspaces satisfying standard approximation assumptions. Numerical examples are provided to support the theoretical findings.\n                  <\/jats:p>","DOI":"10.1007\/s10915-026-03293-w","type":"journal-article","created":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T11:38:42Z","timestamp":1777894722000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Inf\u2013Sup Stable Space\u2013Time Discretization of the Wave Equation Based on a First-Order-In-Time Variational Formulation"],"prefix":"10.1007","volume":"107","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2577-1421","authenticated-orcid":false,"given":"Matteo","family":"Ferrari","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1368-2883","authenticated-orcid":false,"given":"Ilaria","family":"Perugia","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1351-8656","authenticated-orcid":false,"given":"Enrico","family":"Zampa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,5,4]]},"reference":[{"issue":"304","key":"3293_CR1","doi-asserted-by":"publisher","first-page":"549","DOI":"10.1090\/mcom\/3114","volume":"86","author":"A Abdulle","year":"2017","unstructured":"Abdulle, A., Henning, P.: Localized orthogonal decomposition method for the wave equation with a continuum of scales. 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