Since 'degrees' is already plural 'freedom' should not be.
@f}
We note that here and in the following, the indices $k,l$ run over spatial
directions, i.e. $0\le k,l < d$, and that indices $i,j$ run over degrees
-of freedoms.
+of freedom.
The local stiffness matrix on cell $K$ therefore has the following entries:
@f[
revisit some vector-valued problems and show a few techniques that may make it
simpler to actually go through all the stuff shown above, with
FiniteElement::system_to_component_index etc.
-
* element, independent of the cell we are presently on, but for hp DoF
* handlers, this may change from cell to cell.
*
- * @note Since degrees of freedoms only exist on active cells for
+ * @note Since degrees of freedom only exist on active cells for
* hp::DoFHandler (i.e., there is currently no implementation of multilevel
* hp::DoFHandler objects), it does not make sense to query the finite
* element on non-active cells since they do not have finite element spaces
* for this cell. This function is only useful if the DoF handler object
* associated with the current cell is an hp::DoFHandler.
*
- * @note Since degrees of freedoms only exist on active cells for
+ * @note Since degrees of freedom only exist on active cells for
* hp::DoFHandler (i.e., there is currently no implementation of multilevel
* hp::DoFHandler objects), it does not make sense to query active FE
* indices on non-active cells since they do not have finite element spaces
* if the DoF handler object associated with the current cell is an
* hp::DoFHandler.
*
- * @note Since degrees of freedoms only exist on active cells for
+ * @note Since degrees of freedom only exist on active cells for
* hp::DoFHandler (i.e., there is currently no implementation of multilevel
* hp::DoFHandler objects), it does not make sense to assign active FE
* indices to non-active cells since they do not have finite element spaces
* Id_c = project_to_constrained_linear_operator(constraint_matrix, linop);
* @endcode
* and <code>Id_c</code> is the projection to the subspace consisting of all
- * vector entries associated with constrained degrees of freedoms.
+ * vector entries associated with constrained degrees of freedom.
*
* This LinearOperator object is used together with
* constrained_right_hand_side() to build up the following modified system of
* will work on each block separately, i.e. the solutions of the local systems
* corresponding to a degree of freedom of one block will only be used to
* update the degrees of freedom belonging to the same block, but never to
- * update degrees of freedoms of other blocks. A block can be a consecutive
+ * update degrees of freedom of other blocks. A block can be a consecutive
* list of indices, as in the first alternative below, or a nonconsecutive
* list of indices. Of course, we assume that the intersection of each two
* blocks is empty and that the union of all blocks equals the interval
// After setting up all the degrees
- // of freedoms, here are now the
+ // of freedom, here are now the
// differences compared to step-5,
// all of which are related to
// constraints associated with the