DefElement / defelement.com

an encyclopedia of finite element definitions
https://defelement.com
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Add Guzman-Neilan elements #344

Open mscroggs opened 1 week ago

mscroggs commented 1 week ago
pbrubeck commented 1 week ago

To summarize, these are the four families presented in (Guzman & Neilan, 2019), which extend from Bernardi-Raugel and Alfeld-Sorokina

Bernardi-Raugel: (simplex, Pk^d + normal facet bubble, dofs of Pk^d + dofs of RT1) GN first kind (H1-conforming): (simplex, Pk^d + div-free normal facet bubble, same dofs as BR ) GN second kind (H1-conforming): (simplex, C0 Pk(Alfled)^d + div-free normal facet bubble, dofs of Pk(Alfled)^d + dofs of RT1)

Alfeld-Sorokina: (simplex, C0 P2^d(Alfeld) with div in C0 P1(Alfled) , dofs of unsplit P2^d + div at vertices) GN H1(div)-conforming: (simplex, AS + div-free normal facet bubble, dofs of AS + dofs of RT1) Reduced GN H1(div)-conforming: (simplex, AS (vertex-div basis functions only) + GN(k=1), dofs of GN(k=1) + div at vertices)

The GN H1(div)-conforming families only make sense for dimension > 2, they reduce to AS in 2D.