Class to compute the errors between the numerical solution (solution_owned) and the exact solution (solution_ex_owned). More...

#include <compute_errors_DG.hpp>

Public Member Functions
	ComputeErrorsDG (const unsigned int degree, const double stability_coeff, const unsigned int local_dofs, const DoFHandlerDG< basis > &dof_hand, const unsigned int nref_, const std::string &title)
	Constructor. More...

	ComputeErrorsDG (ComputeErrorsDG< basis > &ComputeErrorsDG)=default
	Default copy constructor. More...

	ComputeErrorsDG (const ComputeErrorsDG< basis > &ComputeErrorsDG)=default
	Default const copy constructor. More...

	ComputeErrorsDG (ComputeErrorsDG< basis > &&ComputeErrorsDG)=default
	Default move constructor. More...

void	reinit (const lifex::LinAlg::MPI::Vector &sol_owned, const lifex::LinAlg::MPI::Vector &sol_ex_owned, const std::shared_ptr< dealii::Function< lifex::dim >> &u_ex_input, const std::shared_ptr< dealii::Function< lifex::dim >> &grad_u_ex_input, const char *solution_name_input)
	Reinitialization with new computed and exact solutions. More...

void	compute_errors (std::list< const char * > errors_defs={"inf", "L2", "H1", "DG"})
	Compute errors following the preferences in the list. More...

std::vector< double >	output_errors (std::list< const char * > errors_defs={"inf", "L2", "H1", "DG"}) const
	Output of the errors following the preferences in the list. More...

void	update_datafile () const
	Update the datafile with the new errors. More...

void	initialize_datafile () const
	Create the datafile for the errors. More...

Private Member Functions
void	compute_error_inf ()
	Compute the \(L^\infty\) error. More...

void	compute_error_L2 ()
	Compute the \(L^2\) error. More...

void	compute_error_H1 ()
	Compute the \(H^1\) error. More...

void	compute_error_DG ()
	Compute the \(DG\) error. More...

std::string	get_date () const
	Return the current date and time. More...

void	compute_error_inf ()
	Specialized version for Dubiner basis. More...

Private Attributes
const DoFHandlerDG< basis > &	dof_handler
	Dof handler object of the problem. More...

const unsigned int	n_quad_points
	Number of quadrature points in the volume element. More...

const unsigned int	n_quad_points_face
	Number of quadrature points on the face element. More...

const unsigned int	dofs_per_cell
	Number of degrees of freedom per cell. More...

const double	stability_coefficient
	Stability coefficient, needed for the computation of the \(DG\) error. More...

const unsigned int	fe_degree
	Polynomial degree. More...

const unsigned int	nref
	Number of refinements. More...

const std::string	model_name
	Name of the model. More...

const std::unique_ptr< basis >	basis_ptr
	Pointer to the basis handler. More...

lifex::LinAlg::MPI::Vector	solution_owned
	Computed solution. More...

lifex::LinAlg::MPI::Vector	solution_ex_owned
	Exact solution to compare with the numerical one. More...

std::shared_ptr< dealii::Function< lifex::dim > >	u_ex
	Analytical exact solution. More...

std::shared_ptr< dealii::Function< lifex::dim > >	grad_u_ex
	Gradient of the analytical exact solution. More...

char *	solution_name
	String that contains the solution name (to write on output files, default "u"). More...

std::array< double, 4 >	errors
	Array that contains the current errors (in order, \(L^\infty\), \(L^2\), \(H^1\), \(DG\)). More...

std::shared_ptr< DUBFEMHandler< basis > >	dub_fem_values
	Member to compute conversion to FEM basis, needed for L^inf error. More...

Detailed Description

template<class basis>
class ComputeErrorsDG< basis >

Class to compute the errors between the numerical solution (solution_owned) and the exact solution (solution_ex_owned).

Four definitions of error are implemented:

\[ \|u-u_h\|_{L^\infty(\Omega)}:= \sup_{x\in \Omega} |u(x)-u_h(x)| \]

\[ \|u-u_h\|_{L^2(\Omega)}^2 := \int_{\Omega} |u(x)-u_h(x)|^2 \, dx \]

\[ \|u-u_h\|_{H^1(\Omega)}^2 := \|u-u_h\|_{L^2(\Omega)}^2 + \|\nabla u-\nabla u_h\|_{L^2(\Omega)}^2 \]

\[ \|u-u_h\|_{DG(\Omega)}^2 := \|\nabla u-\nabla u_h\|_{L^2(\Omega)}^2 +\gamma \|[[ u- u_h]]\|_{L^2(\mathcal{F})}^2 \]

where \(\gamma \) is the stability coefficient and the \(L^2(\mathcal{F}) \) norm is computed on the faces instead of the volume. Furthermore, the class can create and update a datafile containing the errors from different simulations that has been previously run with different polynomial orders and grid refinements.

Definition at line 71 of file compute_errors_DG.hpp.

Constructor & Destructor Documentation

◆ ComputeErrorsDG() [1/4]

template<class basis >

ComputeErrorsDG< basis >::ComputeErrorsDG	(	const unsigned int	degree,
		const double	stability_coeff,
		const unsigned int	local_dofs,
		const DoFHandlerDG< basis > &	dof_hand,
		const unsigned int	nref_,
		const std::string &	title
	)

inline

Constructor.

Definition at line 569 of file compute_errors_DG.hpp.

◆ ComputeErrorsDG() [2/4]

template<class basis >

ComputeErrorsDG< basis >::ComputeErrorsDG ( ComputeErrorsDG< basis > & ComputeErrorsDG )

default

Default copy constructor.

◆ ComputeErrorsDG() [3/4]

template<class basis >

ComputeErrorsDG< basis >::ComputeErrorsDG ( const ComputeErrorsDG< basis > & ComputeErrorsDG )

default

Default const copy constructor.

◆ ComputeErrorsDG() [4/4]

template<class basis >

ComputeErrorsDG< basis >::ComputeErrorsDG ( ComputeErrorsDG< basis > && ComputeErrorsDG )

default

Default move constructor.

Member Function Documentation

◆ compute_error_DG()

template<class basis >

void ComputeErrorsDG< basis >::compute_error_DG

private

Compute the \(DG\) error.

Definition at line 441 of file compute_errors_DG.hpp.

◆ compute_error_H1()

template<class basis >

void ComputeErrorsDG< basis >::compute_error_H1

private

Compute the \(H^1\) error.

Definition at line 375 of file compute_errors_DG.hpp.

◆ compute_error_inf() [1/2]

template<class basis >

void ComputeErrorsDG< basis >::compute_error_inf

private

Compute the \(L^\infty\) error.

Definition at line 298 of file compute_errors_DG.hpp.

◆ compute_error_inf() [2/2]

void ComputeErrorsDG< DUBValues< lifex::dim > >::compute_error_inf ( )

private

Specialized version for Dubiner basis.

Before computing the \(L^\infty\) error, the vector solutions are transformed in terms of FEM coefficients.

Definition at line 310 of file compute_errors_DG.hpp.

◆ compute_error_L2()

template<class basis >

void ComputeErrorsDG< basis >::compute_error_L2

private

Compute the \(L^2\) error.

Definition at line 325 of file compute_errors_DG.hpp.

◆ compute_errors()

template<class basis >

void ComputeErrorsDG< basis >::compute_errors ( std::list< const char * > errors_defs = {"inf", "L2", "H1", "DG"} )

Compute errors following the preferences in the list.

E.g., errors_defs={"L2"} will only compute the \(L^2\) error.

Definition at line 227 of file compute_errors_DG.hpp.

◆ get_date()

template<class basis >

std::string ComputeErrorsDG< basis >::get_date

private

Return the current date and time.

Definition at line 556 of file compute_errors_DG.hpp.

◆ initialize_datafile()

template<class basis >

void ComputeErrorsDG< basis >::initialize_datafile

Create the datafile for the errors.

Definition at line 531 of file compute_errors_DG.hpp.

◆ output_errors()

template<class basis >

std::vector< double > ComputeErrorsDG< basis >::output_errors ( std::list< const char * > errors_defs = {"inf", "L2", "H1", "DG"} ) const

Output of the errors following the preferences in the list.

E.g., errors_defs={"L2"} will only output the \(L^2\) error. The output vector contains the errors in the order of the input list.

Definition at line 272 of file compute_errors_DG.hpp.

◆ reinit()

template<class basis >

void ComputeErrorsDG< basis >::reinit	(	const lifex::LinAlg::MPI::Vector &	sol_owned,
		const lifex::LinAlg::MPI::Vector &	sol_ex_owned,
		const std::shared_ptr< dealii::Function< lifex::dim >> &	u_ex_input,
		const std::shared_ptr< dealii::Function< lifex::dim >> &	grad_u_ex_input,
		const char *	solution_name_input
	)

Reinitialization with new computed and exact solutions.

Definition at line 211 of file compute_errors_DG.hpp.

◆ update_datafile()

template<class basis >

void ComputeErrorsDG< basis >::update_datafile

Update the datafile with the new errors.

Definition at line 569 of file compute_errors_DG.hpp.

Member Data Documentation

◆ basis_ptr

template<class basis >

const std::unique_ptr<basis> ComputeErrorsDG< basis >::basis_ptr

private

Pointer to the basis handler.

Definition at line 183 of file compute_errors_DG.hpp.

◆ dof_handler

template<class basis >

const DoFHandlerDG<basis>& ComputeErrorsDG< basis >::dof_handler

private

Dof handler object of the problem.

Definition at line 157 of file compute_errors_DG.hpp.

◆ dofs_per_cell

template<class basis >

const unsigned int ComputeErrorsDG< basis >::dofs_per_cell

private

Number of degrees of freedom per cell.

Definition at line 168 of file compute_errors_DG.hpp.

◆ dub_fem_values

template<class basis >

std::shared_ptr<DUBFEMHandler<basis> > ComputeErrorsDG< basis >::dub_fem_values

private

Member to compute conversion to FEM basis, needed for L^inf error.

Definition at line 206 of file compute_errors_DG.hpp.

◆ errors

template<class basis >

std::array<double, 4> ComputeErrorsDG< basis >::errors

private

Array that contains the current errors (in order, \(L^\infty\), \(L^2\), \(H^1\), \(DG\)).

Definition at line 203 of file compute_errors_DG.hpp.

◆ fe_degree

template<class basis >

const unsigned int ComputeErrorsDG< basis >::fe_degree

private

Polynomial degree.

Definition at line 174 of file compute_errors_DG.hpp.

◆ grad_u_ex

template<class basis >

std::shared_ptr<dealii::Function<lifex::dim> > ComputeErrorsDG< basis >::grad_u_ex

private

Gradient of the analytical exact solution.

Definition at line 195 of file compute_errors_DG.hpp.

◆ model_name

template<class basis >

const std::string ComputeErrorsDG< basis >::model_name

private

Name of the model.

Definition at line 180 of file compute_errors_DG.hpp.

◆ n_quad_points

template<class basis >

const unsigned int ComputeErrorsDG< basis >::n_quad_points

private

Number of quadrature points in the volume element.

By default: \((degree+2)^{dim}\).

Definition at line 161 of file compute_errors_DG.hpp.

◆ n_quad_points_face

template<class basis >

const unsigned int ComputeErrorsDG< basis >::n_quad_points_face

private

Number of quadrature points on the face element.

By default: \((degree+2)^{dim-1}\).

Definition at line 165 of file compute_errors_DG.hpp.

◆ nref

template<class basis >

const unsigned int ComputeErrorsDG< basis >::nref

private

Number of refinements.

Definition at line 177 of file compute_errors_DG.hpp.

◆ solution_ex_owned

template<class basis >

lifex::LinAlg::MPI::Vector ComputeErrorsDG< basis >::solution_ex_owned

private

Exact solution to compare with the numerical one.

Definition at line 189 of file compute_errors_DG.hpp.

◆ solution_name

template<class basis >

char* ComputeErrorsDG< basis >::solution_name

private

String that contains the solution name (to write on output files, default "u").

Definition at line 199 of file compute_errors_DG.hpp.

◆ solution_owned

template<class basis >

lifex::LinAlg::MPI::Vector ComputeErrorsDG< basis >::solution_owned

private

Computed solution.

Definition at line 186 of file compute_errors_DG.hpp.

◆ stability_coefficient

template<class basis >

const double ComputeErrorsDG< basis >::stability_coefficient

private

Stability coefficient, needed for the computation of the \(DG\) error.

Definition at line 171 of file compute_errors_DG.hpp.

◆ u_ex

template<class basis >

std::shared_ptr<dealii::Function<lifex::dim> > ComputeErrorsDG< basis >::u_ex

private

Analytical exact solution.

Definition at line 192 of file compute_errors_DG.hpp.

The documentation for this class was generated from the following file:

source/compute_errors_DG.hpp

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

template<class basis> class ComputeErrorsDG< basis >

Constructor & Destructor Documentation

◆ ComputeErrorsDG() [1/4]

◆ ComputeErrorsDG() [2/4]

◆ ComputeErrorsDG() [3/4]

◆ ComputeErrorsDG() [4/4]

Member Function Documentation

◆ compute_error_DG()

◆ compute_error_H1()

◆ compute_error_inf() [1/2]

◆ compute_error_inf() [2/2]

◆ compute_error_L2()

◆ compute_errors()

◆ get_date()

◆ initialize_datafile()

◆ output_errors()

◆ reinit()

◆ update_datafile()

Member Data Documentation

◆ basis_ptr

◆ dof_handler

◆ dofs_per_cell

◆ dub_fem_values

◆ errors

◆ fe_degree

◆ grad_u_ex

◆ model_name

◆ n_quad_points

◆ n_quad_points_face

◆ nref

◆ solution_ex_owned

◆ solution_name

◆ solution_owned

◆ stability_coefficient

◆ u_ex

template<class basis>
class ComputeErrorsDG< basis >