From: Graham Harper Date: Thu, 6 Jun 2019 02:44:00 +0000 (-0600) Subject: Update FE_BernardiRaugel summary X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=5998f4808fe93a977ca0361fcb41e8912e24a39c;p=release-papers.git Update FE_BernardiRaugel summary --- diff --git a/9.1/paper.tex b/9.1/paper.tex index 62e3918..f461fd2 100644 --- a/9.1/paper.tex +++ b/9.1/paper.tex @@ -211,10 +211,9 @@ that we briefly outline in the remainder of this section: functions on each edge (in 2d) or face (in 3d). It addresses the fact that the $Q_1^d\times Q_0$ combination is not inf-sup stable (requiring a larger velocity space), and that the $Q_2^d\times Q_0$ combination is - stable but sub-optimal since the velocity space is too large relative to - the pressure space to provide additional accuracy commensurate with the - cost of the large number of velocity unknowns. The BR space is - thus intermediate to the $Q_1^d$ and $Q_2^d$ spaces. + stable but converges with only first-order at the cost of the large + number of velocity unknowns. The BR space is thus intermediate to the + $Q_1^d$ and $Q_2^d$ spaces. The element is currently only implemented for parallelogram meshes due to difficulties associated with the mapping of shape functions: The shape