3-NIRVANA-user-guide/3.1-Code-basics.md

@@ -106,7 +106,7 @@ strong magnetic field and/or very low gas density which allows larger
 integration timesteps. More details: [Physics
 guide](https://gitlab.aip.de/ziegler/NIRVANA/-/tree/master/doc/pdf/PhysicsGuide.pdf).
 Use of the Boris correction is controlled in the header file
-[`nirvanaUser.h`](#user-controllable-macros).
+[`nirvanaUser.h`](3.2-User-interfaces#user-controllable-macros).
 
 #### Magnetic field splitting
 
@@ -120,7 +120,7 @@ guide](https://gitlab.aip.de/ziegler/NIRVANA/-/tree/master/doc/pdf/PhysicsGuide.
 Use of the magnetic field splitting scheme is controlled in the header
 file [`nirvanaUser.h`](#user-controllable-macros) and definition of the
 background magnetic field in module
-[`sourceB0User.c`](#user-defined-background-magnetic-field).
+[`sourceB0User.c`](3.2-User-interfaces#user-defined-background-magnetic-field).
 
 ### Dynamic arrays
 
@@ -405,13 +405,13 @@ individually selected by the user. The standard implementation covers
 the following criteria:
 
 -   derivatives-based (most important in practice):
-    $$\left[\alpha\frac{|\d U|}{|U|+U_\mathrm{ref}}+(1-\alpha)
+    $\left[\alpha\frac{|\d U|}{|U|+U_\mathrm{ref}}+(1-\alpha)
     \frac{|\d^2U|}{|\d U|+{\rm FILTER}\cdot(|U|+U_\mathrm{ref})}\right]
     \left(\frac{\d x^{(l)}}{\d x^{(0)}}\right)^{\xi}
     \left\{\begin{array}{ll}
     >\mathcal{E}_{U}  &\exists U \quad\hbox{refinement}\\
     <0.8\mathcal{E}_{U}  & \forall U \quad\hbox{derefinement}\\
-    \end{array}\right.$$
+    \end{array}\right.$
 
     The criterion is applied to physical variables $U$
     ($=\{\varrho,\mathbf{m},e,\mathbf{B},C_\mathrm{c}\}$). Undivided