{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,24]],"date-time":"2026-08-24T09:36:56Z","timestamp":1787564216598,"version":"build-2736575974"},"reference-count":22,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>A new local interpolation operator, preserving the divergence, is constructed explicitly for the Hsieh\u2013Clough\u2013Tocher divergence-free element. A divergence-free finite element method is applied to the Darcy\u2013Stokes\u2013Brinkman flow in a mixed region of both free and porous media. The method is of optimal order as well for the Darcy flow as for the Stokes flow (which is not the case for most other finite elements). Compared to the existing nonconforming elements, the divergence-free element method provides a continuous solution for the velocity which is also an orthogonal projection within a Hilbert subspace of the true velocity. Numerical tests supporting the theory are presented.<\/jats:p>","DOI":"10.1137\/090751049","type":"journal-article","created":{"date-parts":[[2010,3,10]],"date-time":"2010-03-10T18:14:29Z","timestamp":1268244869000},"page":"855-874","source":"Crossref","is-referenced-by-count":55,"title":["A New Divergence-Free Interpolation Operator with Applications to the Darcy\u2013Stokes\u2013Brinkman Equations"],"prefix":"10.1137","volume":"32","author":[{"given":"Xuejun","family":"Xu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shangyou","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,3,10]]},"reference":[{"key":"R1","unstructured":"D.N. Arnold and J. 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