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Furthermore, we provide a counterexample to the inf-sup stability and hence to existence of a Fortin operator for the $$P_2$$<\/jats:tex-math>\n \n P<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>\u2013$$P_0$$<\/jats:tex-math>\n \n P<\/mml:mi>\n 0<\/mml:mn>\n <\/mml:msub>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and the augmented Taylor\u2013Hood element in 3D.<\/jats:p>","DOI":"10.1007\/s00211-021-01260-1","type":"journal-article","created":{"date-parts":[[2021,12,18]],"date-time":"2021-12-18T03:07:41Z","timestamp":1639796861000},"page":"671-689","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Fortin operator for the Taylor\u2013Hood element"],"prefix":"10.1007","volume":"150","author":[{"given":"L.","family":"Diening","sequence":"first","affiliation":[]},{"given":"J.","family":"Storn","sequence":"additional","affiliation":[]},{"given":"T.","family":"Tscherpel","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,12,18]]},"reference":[{"issue":"4","key":"1260_CR1","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1007\/BF02576171","volume":"21","author":"DN Arnold","year":"1984","unstructured":"Arnold, D.N., Brezzi, F., Fortin, M.: A stable finite element for the Stokes equations. 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