Reference documentation for deal.II version GIT relicensing687gbf51c6da8c 20240521 02:00:02+00:00

Public Types  
using  Derivative = Tensor< 2, dim > 
using  ProjectedDerivative = Tensor< 1, dim > 
Public Member Functions  
double  derivative_norm (const Derivative &d) 
double  derivative_norm (const Derivative &d) 
double  derivative_norm (const Derivative &d) 
Static Public Member Functions  
template<class InputVector , int spacedim>  
static ProjectedDerivative  get_projected_derivative (const FEValues< dim, spacedim > &fe_values, const InputVector &solution, const unsigned int component) 
static double  derivative_norm (const Derivative &d) 
static void  symmetrize (Derivative &derivative_tensor) 
Static Public Attributes  
static const UpdateFlags  update_flags = update_gradients 
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.
Definition at line 189 of file derivative_approximation.cc.
using DerivativeApproximation::internal::SecondDerivative< dim >::Derivative = Tensor<2, dim> 
Declare the data type which holds the derivative described by this class.
Definition at line 202 of file derivative_approximation.cc.
using DerivativeApproximation::internal::SecondDerivative< dim >::ProjectedDerivative = Tensor<1, dim> 
Likewise declare the data type that holds the derivative projected to a certain directions.
Definition at line 208 of file derivative_approximation.cc.

inlinestatic 
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).
Definition at line 252 of file derivative_approximation.cc.

inlinestatic 
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 \(l_2\) norm of vectors. It is also the largest value of the curvature of the solution.
Definition at line 490 of file derivative_approximation.cc.

inlinestatic 
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.
Definition at line 513 of file derivative_approximation.cc.

inline 
Definition at line 281 of file derivative_approximation.cc.

inline 
Definition at line 290 of file derivative_approximation.cc.

inline 
Definition at line 313 of file derivative_approximation.cc.

static 
Declare which data fields have to be updated for the function get_projected_derivative
to work.
Definition at line 196 of file derivative_approximation.cc.