"Non UBC"@en . "DSpace"@en . "Neilan, Michael"@en . "2019-03-17T05:02:44Z"@en . "2018-08-02T16:19"@en . "We develop exact polynomial sequences\non Alfeld splits in any spatial dimension\nand for any polynomial degree.\nAn Alfeld split of a tetrahedron is obtained by\nconnecting the vertices of an $n$-simplex\nwith its barycenter. We show that, on these\ntriangulations, the kernel of the exterior derivative\nhas enhanced smoothness. Byproducts of this theory\ninclude characterizations of discrete divergence-free subspaces\nfor the Stokes problem, commutative projections, and simple\nformulas for the dimensions of smooth polynomial spaces. This is joint work with Guosheng Fu and Johnny Guzm\u00C3\u00A1n."@en . "https://circle.library.ubc.ca/rest/handle/2429/68848?expand=metadata"@en . "37.0"@en . "video/mp4"@en . ""@en . "Author affiliation: University of Pittsburgh"@en . "10.14288/1.0377035"@en . "eng"@en . "Unreviewed"@en . "Vancouver : University of British Columbia Library"@en . "Banff International Research Station for Mathematical Innovation and Discovery"@en . "Attribution-NonCommercial-NoDerivatives 4.0 International"@en . "http://creativecommons.org/licenses/by-nc-nd/4.0/"@en . "Researcher"@en . "BIRS Workshop Lecture Videos (Oaxaca de Ju\u00E1rez (Mexico))"@en . "Mathematics"@en . "Numerical analysis"@en . "Partial differential equations"@en . "Exact smooth piecewise polynomial sequences on Alfeld splits"@en . "Moving Image"@en . "http://hdl.handle.net/2429/68848"@en .