* given function may be, taking into account that a virtual function has
* to be called.
*
- * <li> Projection: compute the <i>L<sup>2</sup></i>-projection of the given
- * function onto the finite element space, i.e. if <i>f</i> is the function
- * to be projected, compute <i>f<sub>h</sub></i> in <i>L<sup>2</sup></i> such
- * that <i>(f<sub>h</sub>,v<sub>h</sub>)=(f,v<sub>h</sub>)</i> for all discrete
- * test functions <i>v<sub>h</sub></i>. This is done through the solution of the
- * linear system of equations $M v = f$ where $M$ is the mass matrix
- * $m_{ij} = \int_\Omega \phi_i(x) \phi_j(x) dx$ and
- * $f_i = \int_\Omega f(x) \phi_i(x) dx$. The solution vector $v$ then is
- * the nodal representation of the projection <i>f<sub>h</sub></i>.
+ * <li> Projection: compute the $L^2$-projection of the given function
+ * onto the finite element space, i.e. if $f$ is the function to be
+ * projected, compute $f_h\in V_h$ such that $(f_h,v_h)=(f,v_h)$ for
+ * all discrete test functions $v_h$. This is done through the
+ * solution of the linear system of equations $M v = f$ where $M$ is
+ * the mass matrix $m_{ij} = \int_\Omega \phi_i(x) \phi_j(x) dx$ and
+ * $f_i = \int_\Omega f(x) \phi_i(x) dx$. The solution vector $v$ then
+ * is the nodal representation of the projection $f_h$. The project()
+ * functions are used in the @ref step_23 "step-23" tutorial program.
*
* In order to get proper results, it be may necessary to treat
* boundary conditions right. Below are listed some cases where this
- * may be needed. If needed, this is done by <i>L<sup>2</sup></i>-projection of
+ * may be needed. If needed, this is done by $L^2$-projection of
* the trace of the given function onto the finite element space
* restricted to the boundary of the domain, then taking this
* information and using it to eliminate the boundary nodes from the
*
* Obviously, the results of the two schemes for projection are
* different. Usually, when projecting to the boundary first, the
- * <i>L<sup>2</sup></i>-norm of the difference between original
+ * $L^2$-norm of the difference between original
* function and projection over the whole domain will be larger
* (factors of five have been observed) while the
- * <i>L<sup>2</sup></i>-norm of the error integrated over the
+ * $L^2$-norm of the error integrated over the
* boundary should of course be less. The reverse should also hold
* if no projection to the boundary is performed.
*
* The @p project_boundary_values function acts similar to the
* @p interpolate_boundary_values function, apart from the fact that it does
* not get the nodal values of boundary nodes by interpolation but rather
- * through the <i>L<sup>2</sup></i>-projection of the trace of the function to the boundary.
+ * through the $L^2$-projection of the trace of the function to the boundary.
*
* The projection takes place on all boundary parts with boundary
* indicators listed in the map (FunctioMap@p ::FunctionMap)
* use of the wrong quadrature formula may show a significantly wrong result
* and care should be taken to chose the right formula.
*
- * The <i>H<sup>1</sup></i> seminorm is the <i>L<sup>2</sup></i>
+ * The $H^1$ seminorm is the $L^2$
* norm of the gradient of the difference. The square of the full
- * <i>H<sup>1</sup></i> norm is the sum of the square of seminorm
- * and the square of the <i>L<sup>2</sup></i> norm.
+ * $H^1$ norm is the sum of the square of seminorm
+ * and the square of the $L^2$ norm.
*
* To get the global <i>L<sup>1</sup></i> error, you have to sum up the
* entries in @p difference, e.g. using
- * <tt>Vector<double>::l1_norm</tt> function. For the global <i>L<sup>2</sup></i>
+ * <tt>Vector<double>::l1_norm</tt> function. For the global $L^2$
* difference, you have to sum up the squares of the entries and
* take the root of the sum, e.g. using
* <tt>Vector<double>::l2_norm</tt>. These two operations
* To get the $L_\infty$ norm, take the maximum of the vector elements, e.g.
* using the <tt>Vector<double>::linfty_norm</tt> function.
*
- * For the global <i>H<sup>1</sup></i> norm and seminorm, the same rule applies as for the
- * <i>L<sup>2</sup></i> norm: compute the $l_2$ norm of the cell error vector.
+ * For the global $H^1$ norm and seminorm, the same rule applies as for the
+ * $L^2$ norm: compute the $l_2$ norm of the cell error vector.
* </ul>
*
* All functions use the finite element given to the DoFHandler object the last