Quadratic serendipity finite elements over convex polyhedra
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DOI: 10.1002/nme.5605
Abstract: Summary The conventional approach to construct quadratic elements for an n sided polygon will yield n(n + 1)/2 shape functions, which increases the computational effort. It is well known that the serendipity elements based on… read more here.
Keywords: quadratic serendipity; serendipity finite; shape functions; convex polyhedra ... See more keywords
On the growth of Lebesgue constants for convex polyhedra
Sign Up to like & getrecommendations! Published in 2017 at "Transactions of the American Mathematical Society"
DOI: 10.1090/tran/7225
Abstract: In the paper, new estimates of the Lebesgue constant $$ \mathcal{L}(W)=\frac1{(2\pi)^d}\int_{\mathbb{T}^d}\bigg|\sum_{{k}\in W\cap \mathbb{Z}^d} e^{i({k},\,{x})}\bigg| {\rm d}{ x} $$ for convex polyhedra $W\subset\mathbb{R}^d$ are obtained. The main result states that if $W$ is a convex polyhedron… read more here.
Keywords: lebesgue constants; growth lebesgue; mathbb; convex polyhedra ... See more keywords