]> https://gitweb.dealii.org/ - dealii.git/commitdiff
erased begin end 756/head
authorNicola Giuliani <ngiuliani@sissa.it>
Thu, 9 Apr 2015 14:09:56 +0000 (16:09 +0200)
committerNicola Giuliani <ngiuliani@sissa.it>
Thu, 9 Apr 2015 14:09:56 +0000 (16:09 +0200)
include/deal.II/base/quadrature_lib.h

index b0ba4d865e4cd76478c848fcfe07f2bbed4025f2..da8cf11af5b8199c5071bcc00f894fd684094aad 100644 (file)
@@ -457,16 +457,16 @@ public:
  * International Journal for Numerical Methods in Engineering, vol 24,
  * pages 959–973. year 1987, the author applies the transformation on the
  * reference cell $[-1, 1]$ getting
\begin{align*} n(1) &= 1, \\ n(-1) &= -1, \\ \frac{dn}{dx} &= 0 \text{ at }
- x = x_0, \\ \frac{d^2n}{dx^2} &= 0 \text{ at  } x = x_0 \end{align*}
@f{align*} n(1) &= 1, \\ n(-1) &= -1, \\ \frac{dn}{dx} &= 0 \text{ at }
+ x = x_0, \\ \frac{d^2n}{dx^2} &= 0 \text{ at  } x = x_0 @f}
  * We get
\begin{align*} a &= \frac{1}{q}, \\ b &= -3 \frac{\bar{\Gamma}}{q}, \\
- c &= 3\frac{\bar{\Gamma}}{q}, \\ d &= -b, \end{align*}
@f{align*} a &= \frac{1}{q}, \\ b &= -3 \frac{\bar{\Gamma}}{q}, \\
+ c &= 3\frac{\bar{\Gamma}}{q}, \\ d &= -b, @f}
  * with
\begin{align*}  \eta^{*} &= \bar{\eta}^2 - 1, \\ \bar{\Gamma}  &= \sqrt[3]{
@f{align*}  \eta^{*} &= \bar{\eta}^2 - 1, \\ \bar{\Gamma}  &= \sqrt[3]{
  \bar{\eta} \eta^{*} + |\eta^{*} | } + \sqrt[3]{ \bar{\eta} \eta^{*} -
  |\eta^{*} | } + \bar{\eta}, \\ q &= (\Gamma-\bar{\Gamma})^3 + \bar{\Gamma}
- \frac{\bar{\Gamma}^2+3}{1+3\bar{\Gamma}^2} \end{align*}
+ \frac{\bar{\Gamma}^2+3}{1+3\bar{\Gamma}^2} @f}
  * Since the library assumes $[0,1]$ as reference interval, we will map
  * these values on the proper reference interval in the implementation.
  *

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