* </p>
*
* The four cells that were originally the corners of a square will give you
- * some troubles during computations, as the jacobian of the transformation
+ * some troubles during computations, as the Jacobian of the transformation
* from the reference cell to those cells will go to zero, affecting the error
* constants of the finite element estimates.
*
* GridTools::regularize_corner_cells(tria);
* tria.refine_global(2);
* @endcode
- * generates a mesh that has a much better behavior w.r.t. the jacobian of
+ * generates a mesh that has a much better behavior w.r.t. the Jacobian of
* the Mapping:
*
* <p ALIGN="center">
// For second derivatives on the real cell, we need the gradient of the
// inverse Jacobian J. This involves some calculus and is done
- // vectorized. If L is the gradient of the jacobian on the unit cell,
+ // vectorized. If L is the gradient of the Jacobian on the unit cell,
// the gradient of the inverse is given by (multidimensional calculus) -
// J * (J * L) * J (the third J is because we need to transform the
// gradient L from the unit to the real cell, and then apply the inverse
// Jacobian). Compare this with 1d with j(x) = 1/k(phi(x)), where j =
- // phi' is the inverse of the jacobian and k is the derivative of the
- // jacobian on the unit cell. Then j' = phi' k'/k^2 = j k' j^2.
+ // phi' is the inverse of the Jacobian and k is the derivative of the
+ // Jacobian on the unit cell. Then j' = phi' k'/k^2 = j k' j^2.
template <int dim, typename Number>
Tensor<1, dim *(dim + 1) / 2, Tensor<1, dim, Number>>
process_jacobian_gradient(const Tensor<2, dim, Number> &inv_jac_permut,
vv,
my_data.jacobian_gradients[0][idx][d][e]);
- // Also store the non-inverse jacobian gradient.
+ // Also store the non-inverse Jacobian gradient.
// the diagonal part of Jacobian gradient comes
// first
for (unsigned int d = 0; d < dim; ++d)
face_data.general_jac[n_q_points][d][e][v];
// we need to add the normal vector here because we
// store both the inverse jacobian and the normal vector
- // times the jacobian; of course, there will be
+ // times the Jacobian; of course, there will be
// different values in their product for normal vectors
// oriented in different ways (the memory saving is
- // still significant); we need to divide by the jacobian
+ // still significant); we need to divide by the Jacobian
// size to get the right scaling
for (unsigned int d = 0; d < dim; ++d)
for (unsigned int v = 0;
[offset + q][d][e]);
}
- // Also store the non-inverse jacobian gradient.
+ // Also store the non-inverse Jacobian gradient.
// the diagonal part of Jacobian gradient comes first.
// jac_grad already has its derivatives reordered,
// so no need to compensate for this here