/**
* This class implements the first family <i>H<sup>curl</sup></i>-conforming,
- * vector-valued polynomials, proposed by J.-C. Nédélec in 1980
+ * vector-valued polynomials, proposed by J.-C. Nédélec in 1980
* (Numer. Math. 35).
*
- * The Nédélec polynomials are constructed such that the curl
+ * The Nédélec polynomials are constructed such that the curl
* is in the tensor product polynomial space <i>Q<sub>k</sub></i>.
* Therefore, the polynomial order of each component must be one
* order higher in the corresponding two directions,
* Q<sub>k+1,k,k+1</sub>, Q<sub>k+1,k+1,k</sub>)</i> in 2D and 3D, resp.
*
* @ingroup Polynomials
- * @author Markus Bürg
+ * @author Markus Bürg
* @date 2009, 2010
*/
template <int dim>
public:
/**
* Constructor. Creates all basis
- * functions for Nédélec polynomials
+ * functions for Nédélec polynomials
* of given degree.
*
* @arg k: the degree of the
- * Nédélec space, which is the degree
+ * Nédélec space, which is the degree
* of the largest tensor product
* polynomial space
* <i>Q<sub>k</sub></i> contained.
/**
* Computes the value and the
* first and second derivatives
- * of each Nédélec
+ * of each Nédélec
* polynomial at @p unit_point.
*
* The size of the vectors must
void compute (const Point<dim> &unit_point, std::vector<Tensor<1, dim> > &values, std::vector<Tensor<2, dim> > &grads, std::vector<Tensor<3, dim> > &grad_grads) const;
/**
- * Returns the number of Nédélec
+ * Returns the number of Nédélec
* polynomials.
*/
unsigned int n () const;
/**
- * Returns the degree of the Nédélec
+ * Returns the degree of the Nédélec
* space, which is one less than
* the highest polynomial degree.
*/
const AnisotropicPolynomials<dim> polynomial_space;
/**
- * Number of Nédélec polynomials.
+ * Number of Nédélec polynomials.
*/
const unsigned int n_pols;
* DGQ_{k}
* @f]
* Consequently, approximation order of
- * the Nedelec space equals the value <i>degree</i> given to the constructor.
+ * the Nédélec space equals the value <i>degree</i> given to the constructor.
* In this scheme, the lowest order element would be created by the call
* FE_Nedelec<dim>(0). Note that this follows the convention of Brezzi and
- * Raviart, though not the one used in the original paper by Nedelec.
+ * Raviart, though not the one used in the original paper by Nédélec.
*
* This class is not implemented for the codimension one case
* (<tt>spacedim != dim</tt>).
* inverse) is needed already to generate the values of the shape
* functions on the cells in real space. This is in contrast to most
* other elements, where you only need the Jacobian for the
- * gradients. Thus, to generate the gradients of Nedelec shape
+ * gradients. Thus, to generate the gradients of Nédélec shape
* functions, one would need to have the derivatives of the inverse of
* the Jacobian matrix.
*
- * Basically, the Nedelec shape functions can be understood as the
+ * Basically, the Nédélec shape functions can be understood as the
* gradients of scalar shape functions on the real cell. They are thus
* the inverse Jacobian matrix times the gradients of scalar shape
- * functions on the unit cell. The gradient of Nedelec shape functions
+ * functions on the unit cell. The gradient of Nédélec shape functions
* is then, by the product rule, the sum of first the derivative (with
* respect to true coordinates) of the inverse Jacobian times the
* gradient (in unit coordinates) of the scalar shape function, plus
* drop this first term.
*
* What this means for the present case: first the computation of
- * gradients of Nedelec shape functions is wrong in general. Second,
+ * gradients of Nédélec shape functions is wrong in general. Second,
* in the following two cases you will not notice this:
*
* - If the cell is a parallelogram, then the usual bi-/trilinear mapping
* and the gradient of the shape functions is computed exactly, since the
* first term is zero.
*
- * - With the Nedelec elements, you will usually want to compute
+ * - With the Nédélec elements, you will usually want to compute
* the curl, not the general derivative tensor. However, the curl of the
* Jacobian vanishes, so for the curl of shape functions the first term
* is irrelevant, and the curl will always be computed correctly even on
* cells onto the father
* cell. According to the
* philosophy of the
- * Nédélec element, this
+ * Nédélec element, this
* restriction operator preserves
* the curl of a function
* weakly.