Fix Latex

Author: srosenbu

docs/benchmarks/linear elasticity/plate-with-hole.md

@@ -7,19 +7,19 @@ We consider the case of an infinite plate with a circular hole in the center. Th
 The solution is given in polar coordinates. Assume that the infinite plate is loaded in $x$-direction, then at
 a point  with polar coordinates $(r,\theta)\in\mathbb R_+ \times \mathbb R$, the polar stress components are given by
 
-\[
+$$
     \begin{aligned}
         \sigma_r &= \frac{p}{2}\left(1-\frac{a^2}{r^2}\right)+\frac{p}{2}\left(1-\frac{a^2}{r^2}\right)\left(1-\frac{3a^2}{r^2}\right)\cos(2\theta)\\
         \sigma_\theta &=\frac{p}{2}\left(1+\frac{a^2}{r^2}\right) - \frac{p}{2}\left(1+\frac{3a^4}{r^4}\right)\cos(2\theta)\\
         \sigma_{r\theta} &= -\frac{p}{2}\left(1-\frac{a^2}{r^2}\right)\left(1+\frac{3a^2}{r^2}\right)\sin(2\theta)
     \end{aligned}
-\]
+$$
 In order to transform this into a practical benchmark, we consider a rectangular subdomain
 of the infinite plate around the hole. The boundary conditions of the subdomain are determined
 from the analytical solution. The example is further reduced by only simulating one quarter
 of the rectangular domain and assuming symmetry conditions at the edges. Let $\Omega =[0,l]^2 \setminus\left\{(x,y) \mid \sqrt{x^2+y^2}<a \right\}$ be the domain of the benchmark example, then the PDE is given by
 
-\[
+$$
     \begin{aligned}
 \mathrm{div}\boldsymbol{\sigma}(\boldsymbol{\varepsilon}(\boldsymbol{u})) &= 0 &\quad \boldsymbol u \in \Omega & \\
 \boldsymbol{\varepsilon}(\boldsymbol u) &= \frac{1}{2}\left(\nabla \boldsymbol u + (\nabla\boldsymbol u)^\top\right) &&\text{Infinitesimal strain}\\
@@ -28,4 +28,4 @@ of the rectangular domain and assuming symmetry conditions at the edges. Let $\O
 \boldsymbol u_x &=0 & x=0& \text{Dirichlet BC}\\
 boldsymbol{n}
 \end{aligned}
-\]
+$$