From: Nicola Giuliani Date: Thu, 9 Apr 2015 14:09:56 +0000 (+0200) Subject: erased begin end X-Git-Tag: v8.3.0-rc1~305^2 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=84546bcc33e46cea22b42ea1e58af7554b9a1951;p=dealii.git erased begin end --- diff --git a/include/deal.II/base/quadrature_lib.h b/include/deal.II/base/quadrature_lib.h index b0ba4d865e..da8cf11af5 100644 --- a/include/deal.II/base/quadrature_lib.h +++ b/include/deal.II/base/quadrature_lib.h @@ -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. *