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

Detailed Description

template<int dim>
class DerivativeApproximation::internal::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.

Definition at line 191 of file derivative_approximation.cc.

Member Typedef Documentation

◆ Derivative

template<int dim>

using DerivativeApproximation::internal::SecondDerivative< dim >::Derivative = Tensor<2, dim>

Declare the data type which holds the derivative described by this class.

Definition at line 204 of file derivative_approximation.cc.

◆ ProjectedDerivative

template<int dim>

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 210 of file derivative_approximation.cc.

Member Function Documentation

◆ get_projected_derivative()

template<int dim>

template<class InputVector , int spacedim>

SecondDerivative< dim >::ProjectedDerivative DerivativeApproximation::internal::SecondDerivative< dim >::get_projected_derivative	(	const FEValues< dim, spacedim > &	fe_values,
		const InputVector &	solution,
		const unsigned int	component
	)

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 254 of file derivative_approximation.cc.

◆ derivative_norm() [1/4]

template<int dim>

double DerivativeApproximation::internal::SecondDerivative< dim >::derivative_norm ( const Derivative & d )

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 492 of file derivative_approximation.cc.