DerivativeApproximation::SecondDerivative< dim > Class Template Reference
List of all members.
Detailed Description
template<int dim>
class DerivativeApproximation::SecondDerivative< dim >
The following class is used to describe the data needed to compute the finite difference approximation to the second derivatives on a cell. See the general documentation of this class for more information on implementational details.
- Author:
- Wolfgang Bangerth, 2000
Member Typedef Documentation
Declare the data type which holds the derivative described by this class.
Likewise declare the data type that holds the derivative projected to a certain directions.
Member Function Documentation
template<int dim>
template<class InputVector , int spacedim>
Given an FEValues object initialized to a cell, and a solution vector, extract the desired derivative at the first quadrature point (which is the only one, as we only evaluate the finite element field at the center of each cell).
Return the norm of the derivative object. Here, for the (symmetric) tensor of second derivatives, we choose the absolute value of the largest eigenvalue, which is the matrix norm associated to the
norm of vectors. It is also the largest value of the curvature of the solution.
If for the present derivative order, symmetrization of the derivative tensor is necessary, then do so on the argument.
For the second derivatives, each entry of the tensor is set to the mean of its value and the value of the transpose element.
Note that this function actually modifies its argument.
Member Data Documentation
Declare which data fields have to be updated for the function get_projected_derivative
to work.
The documentation for this class was generated from the following file: