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We derive a complete a priori error analysis of the discretisation error in space and time, including optimal <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^2(L^2)$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:msup>\n                      <mml:mi>L<\/mml:mi>\n                      <mml:mn>2<\/mml:mn>\n                    <\/mml:msup>\n                    <mml:mrow>\n                      <mml:mo>(<\/mml:mo>\n                      <mml:msup>\n                        <mml:mi>L<\/mml:mi>\n                        <mml:mn>2<\/mml:mn>\n                      <\/mml:msup>\n                      <mml:mo>)<\/mml:mo>\n                    <\/mml:mrow>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-norm error bounds for the velocities. Finally, the theoretical results are substantiated with numerical examples.\n<\/jats:p>","DOI":"10.1007\/s00211-021-01264-x","type":"journal-article","created":{"date-parts":[[2022,1,9]],"date-time":"2022-01-09T10:02:42Z","timestamp":1641722562000},"page":"423-478","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Eulerian time-stepping schemes for the non-stationary Stokes equations on time-dependent domains"],"prefix":"10.1007","volume":"150","author":[{"given":"Erik","family":"Burman","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stefan","family":"Frei","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andre","family":"Massing","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,1,9]]},"reference":[{"key":"1264_CR1","unstructured":"Aln\u00e6s, M., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, ME., Wells, G.N.: The FEniCS project version 1.5. 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