/**
* \brief Mesh of a d-simplex with (d+1) vertices and mesh cells, resp.
*
- * The <code>vertices<code> argument contains a vector with all d+1
- * vertices of the simplex. They must be given in an order such that
+ * The @p vertices argument contains a vector with all d+1 vertices
+ * of the simplex. They must be given in an order such that
* the vectors from the first vertex to each of the others form a
* right-handed system. And I am not happy about the discrimination
* involved here.
*
* The meshes generated in two and three dimensions are
*
- * @image simplex_2d.png
- * @image simplex_3d.png
+ * @image html simplex_2d.png
+ * @image html simplex_3d.png
*
* @author Guido Kanschat
* @date 2015
*
* An example with two by three holes is
*
- * @image cheese_2d.png
+ * @image html cheese_2d.png
*
* @author Guido Kanschat
* @date 2015
*
* Examples in two and three dimensions are
*
- * @image hyper_cross_2d.png
- * @image hyper_cross_3d.png
+ * @image html hyper_cross_2d.png
+ * @image html hyper_cross_3d.png
*
* @author Guido Kanschat
* @date 2015
* @relates LinearOperator
*
* Addition of two linear operators @p first_op and @p second_op given by
- * $(\text{first\_op}+\text{second\_op})x:=\text{first\_op}(x)+\text{second\_op}(x)$
+ * $(\text{first\_op}+\text{second\_op})x := \text{first\_op}(x) + \text{second\_op}(x)$
*
* @ingroup LAOperators
*/
* @relates LinearOperator
*
* Subtraction of two linear operators @p first_op and @p second_op given by
- * $(\text{first\_op}-\text{second\_op})x:=\text{first\_op}(x)-\text{second\_op}(x)$
+ * $(\text{first\_op}-\text{second\_op})x := \text{first\_op}(x) - \text{second\_op}(x)$
*
* @ingroup LAOperators
*/
* @relates LinearOperator
*
* Composition of two linear operators @p first_op and @p second_op given by
- * $(\text{first\_op}*\text{second\_op})x:=\text{first\_op}(\text{second\_op}(x))$
+ * $(\text{first\_op}*\text{second\_op})x := \text{first\_op}(\text{second\_op}(x))$
*
* @ingroup LAOperators
*/
* Ainsworth $ c_F=\frac h{24} $, but this factor is a bit esoteric,
* stemming from interpolation estimates and stability constants which may
* hold for the Poisson problem, but may not hold for more general situations.
- * Alternatively, we consider the case when $ c_F=\frac {h_F}_{2p_F} $,
+ * Alternatively, we consider the case when $ c_F=\frac {h_F}{2p_F} $,
* where $ h_F $ is face diagonal and $ p_F=max(p^+,p^-) $ is the
* maximum polynomial degree of adjacent elements. The choice between the two is
* done by means of the enumerator, provided as the last argument in all functions.
* in the second loop. By doing so we avoid problems to decide with which $h$
* to multiply, that of the cell on the one or that of the cell on the other
* side of the face. Whereas for the hp-estimator the @p map stores integrals
- * multiplied by $\frac {h_f}_{2p_f}$, which are then summed in the second loop.
+ * multiplied by $\frac {h_F}{2p_F}$, which are then summed in the second loop.
*
- * $h$ ($h_f$) is taken to be the greatest length of the diagonals of the cell (face).
+ * $h$ ($h_F$) is taken to be the greatest length of the diagonals of the cell (face).
* For more or less uniform cells (faces) without deformed angles, this coincides
* with the diameter of the cell (face).
*
* <li> The face belongs to a Neumann boundary. In this case, the
* contribution of the face $F\in\partial K$ looks like \f[ n_F\int_F
* \left|g-a\frac{\partial u_h}{\partial n}\right|^2 ds \f] where $g$ is the
- * Neumann boundary function, $n_F=\frac h_{24}$ and $n_F=\frac {h_F}{p}$ for
+ * Neumann boundary function, $n_F=\frac {h}{24}$ and $n_F=\frac {h_F}{p}$ for
* the Kelly and hp-estimator, respectively.
* If the finite element is vector-valued, then
* obviously the function denoting the Neumann boundary conditions needs to be
*/
enum Strategy
{
- //! Kelly error estimator with the factor $\frac h_{24}$.
+ //! Kelly error estimator with the factor $\frac {h}{24}$.
cell_diameter_over_24 = 0,
- //! the boundary residual estimator with the factor $\frac {h_F}_{2 max(p^+,p^-)$.
+ //! the boundary residual estimator with the factor $\frac {h_F}{2 max(p^+,p^-)}$.
face_diameter_over_twice_max_degree
};