fix a bunch of latex formula errors

doc/doxygen/options.dox.in

@@ -190,6 +190,7 @@ PREDEFINED             = DOXYGEN=1 \
                          DEAL_II_ADOLC_WITH_ADVANCED_BRANCHING=1 \
                          DEAL_II_ADOLC_WITH_ATRIG_ERF=1 \
                          DEAL_II_ADOLC_WITH_TAPELESS_REFCOUNTING=1 \
+                         DEAL_II_CXX20_REQUIRES(x)= \
                          DEAL_II_DEPRECATED_EARLY= \
                          DEAL_II_DEPRECATED_EARLY_WITH_COMMENT(x)= \
                          DEAL_II_WITH_ARBORX=1 \

examples/step-24/doc/intro.dox

@@ -156,7 +156,6 @@ From this we obtain the discrete model by introducing a finite number of shape
 functions, and get
 @f{eqnarray*}{
 M\bar{p}^{n}-k \theta M v^n & = & M\bar{p}^{n-1}+k (1-\theta)Mv^{n-1},\\
-
 (-c_0^2k \theta A-c_0 B)\bar{p}^n-Mv^{n} & = &
 (c_0^2k(1-\theta)A-c_0B)\bar{p}^{n-1}-Mv^{n-1}+c_0^2k(\theta F^{n}+(1-\theta)F^{n-1}).
 @f}

examples/step-33/step-33.cc

@@ -1631,7 +1631,7 @@ namespace Step33
   // $\mathbf{z}_i$ is the $i$th vector valued test function.
   //   Furthermore, the scalar product
   // $\left(\mathbf{F}(\mathbf{w}), \nabla\mathbf{z}_i\right)_K$ is
-  // understood as $\int_K \sum_{c=1}^{\text{n_components}}
+  // understood as $\int_K \sum_{c=1}^{\text{n\_components}}
   // \sum_{d=1}^{\text{dim}} \mathbf{F}(\mathbf{w})_{cd}
   // \frac{\partial z^c_i}{x_d}$ where $z^c_i$ is the $c$th component of
   // the $i$th test function.
@@ -1810,21 +1810,21 @@ namespace Step33
     // @f{eqnarray*}{
     // R_i &=&
     // \left(\frac{(\mathbf{w}_{n+1} -
-    // \mathbf{w}_n)_{\text{component_i}}}{\delta
-    // t},(\mathbf{z}_i)_{\text{component_i}}\right)_K
+    // \mathbf{w}_n)_{\text{component\_i}}}{\delta
+    // t},(\mathbf{z}_i)_{\text{component\_i}}\right)_K
     // \\ &-& \sum_{d=1}^{\text{dim}} \left(  \theta \mathbf{F}
-    // ({\mathbf{w}^k_{n+1}})_{\text{component_i},d} + (1-\theta)
-    // \mathbf{F} ({\mathbf{w}_{n}})_{\text{component_i},d}  ,
-    // \frac{\partial(\mathbf{z}_i)_{\text{component_i}}} {\partial
+    // ({\mathbf{w}^k_{n+1}})_{\text{component\_i},d} + (1-\theta)
+    // \mathbf{F} ({\mathbf{w}_{n}})_{\text{component\_i},d}  ,
+    // \frac{\partial(\mathbf{z}_i)_{\text{component\_i}}} {\partial
     // x_d}\right)_K
     // \\ &+& \sum_{d=1}^{\text{dim}} h^{\eta} \left( \theta \frac{\partial
-    // (\mathbf{w}^k_{n+1})_{\text{component_i}}}{\partial x_d} + (1-\theta)
-    // \frac{\partial (\mathbf{w}_n)_{\text{component_i}}}{\partial x_d} ,
-    // \frac{\partial (\mathbf{z}_i)_{\text{component_i}}}{\partial x_d}
+    // (\mathbf{w}^k_{n+1})_{\text{component\_i}}}{\partial x_d} + (1-\theta)
+    // \frac{\partial (\mathbf{w}_n)_{\text{component\_i}}}{\partial x_d} ,
+    // \frac{\partial (\mathbf{z}_i)_{\text{component\_i}}}{\partial x_d}
     // \right)_K
-    // \\ &-& \left( \theta\mathbf{G}({\mathbf{w}^k_n+1} )_{\text{component_i}}
-    // + (1-\theta)\mathbf{G}({\mathbf{w}_n})_{\text{component_i}} ,
-    // (\mathbf{z}_i)_{\text{component_i}} \right)_K ,
+    // \\ &-& \left( \theta\mathbf{G}({\mathbf{w}^k_n+1} )_{\text{component\_i}}
+    // + (1-\theta)\mathbf{G}({\mathbf{w}_n})_{\text{component\_i}} ,
+    // (\mathbf{z}_i)_{\text{component\_i}} \right)_K ,
     // @f}
     // where integrals are
     // understood to be evaluated through summation over quadrature points.

examples/step-42/doc/intro.dox

@@ -321,7 +321,7 @@ method for the contact. It works as follows:
  Here,
  $P_{\mathcal{A}}(U)$ is the projection of the active
  components in $\mathcal{A}$ to the gap
- @f{gather*}P_{\mathcal{A}}(U)_p \dealcoloneq \begin{cases}{
+ @f{gather*}P_{\mathcal{A}}(U)_p \dealcoloneq \begin{cases}
  U_p, & \textrm{if}\quad p\notin\mathcal{A}\\
  g_{h,p}, & \textrm{if}\quad
  p\in\mathcal{A},
@@ -346,7 +346,7 @@ we can choose $B$ to be a matrix that has only one entry per row,
 set strategy for non-linear multibody contact problems, Comput. Methods Appl. Mech. Engrg.
 194, 2005, pp. 3147-3166).
 The vector $G$ is defined by a suitable approximation $g_h$ of the gap $g$
-@f{gather*}G_p = \begin{cases}{
+@f{gather*}G_p = \begin{cases}
 g_{h,p}, & \text{if}\quad p\in\mathcal{S}\\
 0, & \text{if}\quad p\notin\mathcal{S}.
 \end{cases}@f}

examples/step-56/step-56.cc

@@ -451,8 +451,7 @@ namespace Step56
     , solver_type(solver_type)
     , triangulation(Triangulation<dim>::maximum_smoothing)
     ,
-    // Finite element for the velocity only -- we choose the
-    // $Q_{\text{pressure_degree}}^d$ element:
+    // Finite element for the velocity only:
     velocity_fe(FE_Q<dim>(pressure_degree + 1) ^ dim)
     ,
     // Finite element for the whole system:

examples/step-79/doc/intro.dox

@@ -100,7 +100,6 @@ following:
   0<\rho_{\min}\leq \rho(x) \leq 1,
 @f]
 @f[
-
   \nabla \cdot \boldsymbol{\sigma}(\rho) + \mathbf{F} = 0 \quad \text{on } \Omega
 @f]
 The final constraint, the balance of linear momentum (which we will refer to as the elasticity equation),
@@ -300,7 +299,6 @@ where forces are applied, and Neumann boundary conditions are used.
 @f[
   \int_\Omega -d_\varrho z_1 + d_\varrho z_2 + H(d_\varrho)y_2 d\Omega= 0\;\;\forall
   d_\varrho
-
 @f]
 </li>
 <li> Primal Feasibility:

examples/step-81/doc/intro.dox

@@ -184,16 +184,14 @@ $\varepsilon_0$ and $\mu_0$ as
 We use the free-space wave number $k_0 = \omega\sqrt{\varepsilon_0\mu_0}$ and
 the dipole strength, $J_0$ to arrive at the following rescaling of the vector
 fields and coordinates:
-@f[
-\begin{align*}
+@f{align*}{
 \hat{x} = k_0x, &\qquad
 \hat{\nabla} = \frac{1}{k_0}\nabla,\\
 \hat{\mathbf{H}} = \frac{k_0}{J_0}\mu^{-1}\mathbf{H},&\qquad
 \hat{\mathbf{E}} = \frac{k_0^2}{\omega\mu_0 J_0}\mathbf{E},\\
 \hat{\mathbf{J}}_a = \frac{1}{J_0}\mathbf{J}_a,&\qquad
 \hat{\mathbf{M}}_a = \frac{k_0}{\omega\mu_0 J_0}\mathbf{M}_a.
-\end{align*}
-@f]
+@f}
 
 Finally, the interface conductivity is rescaled as
 @f[
@@ -286,7 +284,7 @@ i\int_\Omega \mathbf{J}_a \cdot \bar{\varphi}\;\text{d}x
 
 Assume that $\sigma_r^{\Sigma} \in L^{\infty}(\Sigma)^{2\times 2}$ is matrix-valued
 and symmetric, and has a semidefinite real and complex part. Let $\varepsilon_r$
-be a smooth scalar function with $–\text{Im}(\varepsilon_r) = 0$, or
+be a smooth scalar function with $-\text{Im}(\varepsilon_r) = 0$, or
 $\text{Im}(\varepsilon_r)\ge c > 0$ in $\Omega$. $\mu_r^{-1}$ is a smooth scalar
 such that $\sqrt{\mu_r^{-1}\varepsilon_r}$ is real valued and strictly positive
 in $\partial\Omega$.

examples/step-87/doc/intro.dox

@@ -44,7 +44,7 @@ the evaluation of the solution at an arbitrary point boils down to a cell-local
 evaluation
 @f[
 u(\boldsymbol{x}_q) = \sum_{i} \hat{N}^K_i(\hat{\boldsymbol{x}}_q) u_i^K
-\quad\text{with}\quad i\in[0,n_{\text{dofs_per_cell}}),
+\quad\text{with}\quad i\in[0,n_{\text{dofs\_per\_cell}}),
 @f]
 with $\hat{N}^K_i$ being the shape functions defined on the reference cell and
 $u_i^{K}$ the solution coefficients

examples/step-87/step-87.cc

@@ -866,7 +866,7 @@ namespace Step87
         // =
         // \sum_i\text{tr}\left({\nabla \boldsymbol{N}_i (\boldsymbol{x}_q)
         // \boldsymbol n_i}\right)
-        // \;\text{with}\; i\in[0,n_{\text{dofs_per_cell}}),
+        // \;\text{with}\; i\in[0,n_{\text{dofs\_per\_cell}}),
         // @f]
         // which we can apply since the immersed mesh is consistently
         // orientated. The surface tension coefficient is set to 1 for the

include/deal.II/fe/fe_coupling_values.h

@@ -519,12 +519,12 @@ enum class QuadratureCouplingType
  *
  * \f[
  * \phi_{1,i}(x) = \begin{cases} v_i(x) & \text{ if } i \in [0,n_l) \\
- * 0 & \text{ if ) i \in [n_1, n_1+n_2] \end{cases},\quad \phi_{1,i}(x) =
+ * 0 & \text{ if } i \in [n_1, n_1+n_2] \end{cases},\quad \phi_{1,i}(x) =
  * \begin{cases} 0(x) & \text{ if } i \in [0,n_1) \\
- * w_{i-n_1}(x) & \text{ if ) i \in [n_1, n_1+n_2] \end{cases},
+ * w_{i-n_1}(x) & \text{ if } i \in [n_1, n_1+n_2] \end{cases},
  * \f]
  *
- * where $phi_{1,i}$ is the first basis function with index $i$ and $n_{1,2}$
+ * where $\phi_{1,i}$ is the first basis function with index $i$ and $n_{1,2}$
  * are the number of local dofs on the first and second FEValuesBase objects.
  *
  * This enum is used in the constructor of FECouplingValues to specify how to

include/deal.II/integrators/maxwell.h

@@ -72,15 +72,17 @@ namespace LocalIntegrators
      * \partial_1\partial_2 u_2 - \partial_2^2 u_1 \\
      * \partial_1\partial_2 u_1 - \partial_1^2 u_2
      * \end{pmatrix}
-     *
+     * @f]
+     * and
+     * @f[
      * \nabla\times\nabla\times \mathbf u = \begin{pmatrix}
      * \partial_1\partial_2 u_2 + \partial_1\partial_3 u_3
      * - (\partial_2^2+\partial_3^2) u_1 \\
      * \partial_2\partial_3 u_3 + \partial_2\partial_1 u_1
      * - (\partial_3^2+\partial_1^2) u_2 \\
      * \partial_3\partial_1 u_1 + \partial_3\partial_2 u_2
      * - (\partial_1^2+\partial_2^2) u_3
-     * \end{pmatrix}
+     * \end{pmatrix}.
      * @f]
      *
      * @note The third tensor argument is not used in two dimensions and can