getfem-commits
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## [Getfem-commits] (no subject)

 From: Yves Renard Subject: [Getfem-commits] (no subject) Date: Thu, 1 Jun 2017 04:49:53 -0400 (EDT)

branch: devel-yves
commit 459e21accbb8223fb970237da2742de2b0177522
Date:   Wed May 31 12:14:09 2017 +0200

minor change
---
doc/sphinx/source/userdoc/appendixA.rst | 33 +++++++++++++++++----------------
1 file changed, 17 insertions(+), 16 deletions(-)

diff --git a/doc/sphinx/source/userdoc/appendixA.rst
b/doc/sphinx/source/userdoc/appendixA.rst
index 77e42c1..7a45b88 100644
--- a/doc/sphinx/source/userdoc/appendixA.rst
+++ b/doc/sphinx/source/userdoc/appendixA.rst
@@ -1333,7 +1333,7 @@ Lagrange elements on 3D pyramid

The associated geometric transformations are "GT_PYRAMID(K)" for K = 1 or
2. The associated integration methods "IM_PYRAMID(im)" where im is an
integration method on a hexahedron (or alternatively
"IM_PYRAMID_COMPOSITE(im)" where im is an integration method on a
tetrahedron, but it is theoretically less accurate)
-The shape functions are not polynomial ones but rational fractions. For the
first degree :
+The shape functions are not polynomial ones but rational fractions. For the
first degree the shape functions read:

.. math::

@@ -1349,26 +1349,27 @@ For the second degree, setting

.. math::

-   \xi_0 = \Frac{1-z-x}{2}, ~~~\xi_1 = \Frac{1-z-y}{2}, ~~~\xi_2 =
\Frac{1-z+x}{2}, ~~~\xi_3 = \Frac{1-z+y}{2},
+   \xi_0 = \Frac{1-z-x}{2}, ~~~\xi_1 = \Frac{1-z-y}{2}, ~~~\xi_2 =
\Frac{1-z+x}{2}, ~~~\xi_3 = \Frac{1-z+y}{2}, ~~~\xi_4 = z,

.. math::

\begin{array}{l}
-   \widehat{\varphi}_{0}(x,y,z) = \Frac{\xi_0
\xi_1}{(1-z)^2}((1-z-2\xi_0)(1-z-2\xi_1) -z(1-z)), \\
-   \widehat{\varphi}_{1}(x,y,z) =
4\Frac{\xi_0\xi_1\xi_2}{(1-z)^2}(2\xi_1-(1-z)), \\
-   \widehat{\varphi}_{2}(x,y,z) = \Frac{\xi_1
\xi_2}{(1-z)^2}((1-z-2\xi_1)(1-z-2\xi_2) -z(1-z)), \\
-   \widehat{\varphi}_{3}(x,y,z) =
4\Frac{\xi_3\xi_0\xi_1}{(1-z)^2}(2\xi_0-(1-z)), \\
-   \widehat{\varphi}_{4}(x,y,z) = 16\Frac{\xi_0\xi_1\xi_2\xi_3}{(1-z)^2}, \\
-   \widehat{\varphi}_{5}(x,y,z) =
4\Frac{\xi_1\xi_2\xi_3}{(1-z)^2}(2\xi_2-(1-z)), \\
-   \widehat{\varphi}_{6}(x,y,z) = \Frac{\xi_3
\xi_0}{(1-z)^2}((1-z-2\xi_3)(1-z-2\xi_0) -z(1-z)), \\
-   \widehat{\varphi}_{7}(x,y,z) =
4\Frac{\xi_2\xi_3\xi_0}{(1-z)^2}(2\xi_3-(1-z)), \\
-   \widehat{\varphi}_{8}(x,y,z) = \Frac{\xi_2
\xi_3}{(1-z)^2}((1-z-2\xi_2)(1-z-2\xi_3) -z(1-z)), \\
-   \widehat{\varphi}_{9}(x,y,z) = 4\Frac{z}{1-z}\xi_0\xi_1, \\
-   \widehat{\varphi}_{10}(x,y,z) = 4\Frac{z}{1-z}\xi_1\xi_2,  \\
-   \widehat{\varphi}_{11}(x,y,z) = 4\Frac{z}{1-z}\xi_3\xi_0,  \\
-   \widehat{\varphi}_{12}(x,y,z) = 4\Frac{z}{1-z}\xi_2\xi_3,  \\
-   \widehat{\varphi}_{13}(x,y,z) = z(2z-1). \\
+   \widehat{\varphi}_{0}(x,y,z) = \Frac{\xi_0
\xi_1}{(1-\xi_4)^2}((1-\xi_4-2\xi_0)(1-\xi_4-2\xi_1) -\xi_4(1-\xi_4)), \\
+   \widehat{\varphi}_{1}(x,y,z) =
4\Frac{\xi_0\xi_1\xi_2}{(1-\xi_4)^2}(2\xi_1-(1-\xi_4)), \\
+   \widehat{\varphi}_{2}(x,y,\xi_4) = \Frac{\xi_1
\xi_2}{(1-\xi_4)^2}((1-\xi_4-2\xi_1)(1-\xi_4-2\xi_2) -\xi_4(1-\xi_4)), \\
+   \widehat{\varphi}_{3}(x,y,z) =
4\Frac{\xi_3\xi_0\xi_1}{(1-\xi_4)^2}(2\xi_0-(1-\xi_4)), \\
+   \widehat{\varphi}_{4}(x,y,z) = 16\Frac{\xi_0\xi_1\xi_2\xi_3}{(1-\xi_4)^2},
\\
+   \widehat{\varphi}_{5}(x,y,z) =
4\Frac{\xi_1\xi_2\xi_3}{(1-\xi_4)^2}(2\xi_2-(1-\xi_4)), \\
+   \widehat{\varphi}_{6}(x,y,z) = \Frac{\xi_3
\xi_0}{(1-\xi_4)^2}((1-\xi_4-2\xi_3)(1-\xi_4-2\xi_0) -\xi_4(1-\xi_4)), \\
+   \widehat{\varphi}_{7}(x,y,z) =
4\Frac{\xi_2\xi_3\xi_0}{(1-\xi_4)^2}(2\xi_3-(1-\xi_4)), \\
+   \widehat{\varphi}_{8}(x,y,z) = \Frac{\xi_2
\xi_3}{(1-\xi_4)^2}((1-\xi_4-2\xi_2)(1-\xi_4-2\xi_3) -\xi_4(1-\xi_4)), \\
+   \widehat{\varphi}_{9}(x,y,z) = 4\Frac{\xi_4}{1-\xi_4}\xi_0\xi_1, \\
+   \widehat{\varphi}_{10}(x,y,z) = 4\Frac{\xi_4}{1-\xi_4}\xi_1\xi_2,  \\
+   \widehat{\varphi}_{11}(x,y,z) = 4\Frac{\xi_4}{1-\xi_4}\xi_3\xi_0,  \\
+   \widehat{\varphi}_{12}(x,y,z) = 4\Frac{\xi_4}{1-\xi_4}\xi_2\xi_3,  \\
+   \widehat{\varphi}_{13}(x,y,z) = \xi_4(2\xi_4-1). \\
\end{array}

.. list-table:: Continuous Lagrange element of order 0, 1 or 2
"FEM_PYRAMID_LAGRANGE(K)"