{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,13]],"date-time":"2026-06-13T06:50:57Z","timestamp":1781333457290,"version":"3.54.1"},"reference-count":18,"publisher":"American Mathematical Society (AMS)","issue":"275","license":[{"start":{"date-parts":[[2012,2,28]],"date-time":"2012-02-28T00:00:00Z","timestamp":1330387200000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We construct wavelet Riesz bases for the usual Sobolev spaces of divergence free functions on\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"left-parenthesis 0 comma 1 right-parenthesis Superscript n\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mn>0<\/mml:mn>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                            <mml:msup>\n                              <mml:mo stretchy=\"false\">)<\/mml:mo>\n                              <mml:mi>n<\/mml:mi>\n                            <\/mml:msup>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">(0,1)^n<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    that have vanishing normals at the boundary. We give a simultaneous space-time variational formulation of the instationary Stokes equations that defines a boundedly invertible mapping between a Bochner space and the dual of another Bochner space. By equipping these Bochner spaces by tensor products of temporal and divergence-free spatial wavelets, the Stokes problem is rewritten as an equivalent well-posed bi-infinite matrix vector equation. This equation can be solved with an adaptive wavelet method in linear complexity with best possible rate, that, under some mild Besov smoothness conditions, is nearly independent of the space dimension. For proving one of the intermediate results, we construct an eigenfunction basis of the stationary Stokes operator.\n                  <\/p>","DOI":"10.1090\/s0025-5718-2011-02471-3","type":"journal-article","created":{"date-parts":[[2011,3,1]],"date-time":"2011-03-01T14:36:20Z","timestamp":1298990180000},"page":"1499-1523","source":"Crossref","is-referenced-by-count":18,"title":["Divergence-free wavelet bases on the hypercube: Free-slip boundary conditions, and applications for solving the instationary Stokes equations"],"prefix":"10.1090","volume":"80","author":[{"given":"Rob","family":"Stevenson","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"14","published-online":{"date-parts":[[2011,2,28]]},"reference":[{"key":"1","doi-asserted-by":"crossref","unstructured":"[CS10] N.G. Chegini and R.P. Stevenson. Adaptive wavelets schemes for parabolic problems: Sparse matrices and numerical results. 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Mech.","ISSN":"https:\/\/id.crossref.org\/issn\/0044-2267","issn-type":"print"},{"issue":"6","key":"12","doi-asserted-by":"publisher","first-page":"3125","DOI":"10.1090\/S0002-9947-08-04827-7","article-title":"On the analyticity of the semigroup generated by the Stokes operator with Neumann-type boundary conditions on Lipschitz subdomains of Riemannian manifolds","volume":"361","author":"Mitrea, Marius","year":"2009","journal-title":"Trans. Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9947","issn-type":"print"},{"issue":"1","key":"13","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1007\/s00365-005-0609-6","article-title":"Best \ud835\udc41 term approximation spaces for tensor product wavelet bases","volume":"24","author":"Nitsche, P\u00e1l-Andrej","year":"2006","journal-title":"Constr. 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Kunoth, editors, Multiscale, Nonlinear and Adaptive Approximation: Dedicated to Wolfgang Dahmen on the Occasion of his 60th Birthday, pages 543\u2013598. Springer, 2009."},{"key":"17","series-title":"Studies in Mathematics and its Applications","isbn-type":"print","volume-title":"Navier-Stokes equations","volume":"2","author":"Temam, Roger","year":"1979","ISBN":"https:\/\/id.crossref.org\/isbn\/0444853073"},{"key":"18","series-title":"Mathematische Leitf\\\"{a}den. 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