mfem::KellyErrorEstimator Class Reference

The KellyErrorEstimator class provides a fast error indication strategy for smooth scalar parallel problems. More...

#include <estimators.hpp>

Inheritance diagram for mfem::KellyErrorEstimator:

Collaboration diagram for mfem::KellyErrorEstimator:

Public Types
using	ElementCoefficientFunction = std::function< double(Mesh *, const int)>
	Function type to compute the local coefficient hₑ of an element. More...
using	FaceCoefficientFunction = std::function< double(Mesh *, const int, const bool)>
	Function type to compute the local coefficient hₖ of a face. The third argument is true for shared faces and false for local faces. More...

Public Member Functions
	KellyErrorEstimator (BilinearFormIntegrator &di_, GridFunction &sol_, FiniteElementSpace &flux_fes_, const Array< int > &attributes_=Array< int >())
	Construct a new KellyErrorEstimator object for a scalar field. More...
	KellyErrorEstimator (BilinearFormIntegrator &di_, GridFunction &sol_, FiniteElementSpace *flux_fes_, const Array< int > &attributes_=Array< int >())
	Construct a new KellyErrorEstimator object for a scalar field. More...
	~KellyErrorEstimator ()
const Vector &	GetLocalErrors () override
	Get a Vector with all element errors. More...
void	Reset () override
	Reset the error estimator. More...
virtual double	GetTotalError () const override
	Return the total error from the last error estimate. More...
void	SetElementCoefficientFunction (ElementCoefficientFunction compute_element_coefficient_)
	Change the method to compute hₑ on a per-element basis. More...
void	SetFaceCoefficientFunction (FaceCoefficientFunction compute_face_coefficient_)
	Change the method to compute hₖ on a per-element basis. More...
void	ResetCoefficientFunctions ()
	Change the coefficients back to default as described above. More...
Public Member Functions inherited from mfem::ErrorEstimator
virtual	~ErrorEstimator ()
	Destruct the error estimator. More...
Public Member Functions inherited from mfem::AbstractErrorEstimator
virtual	~AbstractErrorEstimator ()

Detailed Description

The KellyErrorEstimator class provides a fast error indication strategy for smooth scalar parallel problems.

The Kelly error indicator is based on the following papers:

[1] Kelly, D. W., et al. "A posteriori error analysis and adaptive processes in the finite element method: Part I—Error analysis." International journal for numerical methods in engineering 19.11 (1983): 1593-1619.

[2] De SR Gago, J. P., et al. "A posteriori error analysis and adaptive processes in the finite element method: Part II—Adaptive mesh refinement." International journal for numerical methods in engineering 19.11 (1983): 1621-1656.

It can be roughly described by: ||∇(u-uₕ)||ₑ ≅ √( C hₑ ∑ₖ (hₖ ∫ |J[∇uₕ]|²) dS ) where "e" denotes an element, ||⋅||ₑ the corresponding local norm and k the corresponding faces. u is the analytic solution and uₕ the discretized solution. hₖ and hₑ are factors dependent on the face and element geometry. J is the jump function, i.e. the difference between the limits at each point for each side of the face. A custom method to compute hₖ can be provided. It is also possible to estimate the error only on a subspace by feeding this class an attribute array describing the subspace.

Note

This algorithm is appropriate only for problems with scalar diffusion coefficients (e.g. Poisson problems), because it measures only the flux of the gradient of the discrete solution. The current implementation also does not include the volume term present in Equation 75 of Kelly et al [1]. Instead, it includes only the flux term recommended in Equation 82. The current implementation also does not include the constant factor "C". It furthermore assumes that the approximation error at the boundary is small enough, as the implementation ignores boundary faces.

Definition at line 555 of file estimators.hpp.

Member Typedef Documentation

ElementCoefficientFunction

using mfem::KellyErrorEstimator::ElementCoefficientFunction = std::function<double(Mesh*, const int)>

Function type to compute the local coefficient hₑ of an element.

Definition at line 560 of file estimators.hpp.

FaceCoefficientFunction

using mfem::KellyErrorEstimator::FaceCoefficientFunction = std::function<double(Mesh*, const int, const bool)>

Function type to compute the local coefficient hₖ of a face. The third argument is true for shared faces and false for local faces.

Definition at line 564 of file estimators.hpp.

Constructor & Destructor Documentation

KellyErrorEstimator() [1/2]

mfem::KellyErrorEstimator::KellyErrorEstimator	(	BilinearFormIntegrator &	di_,
		GridFunction &	sol_,
		FiniteElementSpace &	flux_fes_,
		const Array< int > &	attributes_ = Array<int>()
	)

Construct a new KellyErrorEstimator object for a scalar field.

Parameters

di_	The bilinearform to compute the interface flux.
sol_	The solution field whose error is to be estimated.
flux_fes_	The finite element space for the interface flux.
attributes_	The attributes of the subdomain(s) for which the error should be estimated. An empty array results in estimating the error over the complete domain.

Definition at line 64 of file estimators.cpp.

KellyErrorEstimator() [2/2]

mfem::KellyErrorEstimator::KellyErrorEstimator	(	BilinearFormIntegrator &	di_,
		GridFunction &	sol_,
		FiniteElementSpace *	flux_fes_,
		const Array< int > &	attributes_ = Array<int>()
	)

Construct a new KellyErrorEstimator object for a scalar field.

Parameters

di_	The bilinearform to compute the interface flux.
sol_	The solution field whose error is to be estimated.
flux_fes_	The finite element space for the interface flux.
attributes_	The attributes of the subdomain(s) for which the error should be estimated. An empty array results in estimating the error over the complete domain.

Definition at line 80 of file estimators.cpp.

~KellyErrorEstimator()

mfem::KellyErrorEstimator::~KellyErrorEstimator

(

)

Definition at line 96 of file estimators.cpp.

Member Function Documentation

GetLocalErrors()

const Vector& mfem::KellyErrorEstimator::GetLocalErrors ( )

inlineoverridevirtual

Get a Vector with all element errors.

Implements mfem::ErrorEstimator.

Definition at line 652 of file estimators.hpp.

GetTotalError()

virtual double mfem::KellyErrorEstimator::GetTotalError ( ) const

inlineoverridevirtual

Return the total error from the last error estimate.

Note

This method is optional for derived classes to override and the base class implementation simply returns 0.

Reimplemented from mfem::ErrorEstimator.

Definition at line 664 of file estimators.hpp.

Reset()

void mfem::KellyErrorEstimator::Reset ( )

inlineoverridevirtual

Reset the error estimator.

Implements mfem::ErrorEstimator.

Definition at line 662 of file estimators.hpp.

ResetCoefficientFunctions()

void mfem::KellyErrorEstimator::ResetCoefficientFunctions

(

)

Change the coefficients back to default as described above.

Definition at line 104 of file estimators.cpp.

SetElementCoefficientFunction()

void mfem::KellyErrorEstimator::SetElementCoefficientFunction ( ElementCoefficientFunction  compute_element_coefficient_ )

inline

Change the method to compute hₑ on a per-element basis.

Parameters

compute_element_coefficient_

A function taking a mesh and an element index to compute the local hₑ for the element.

Definition at line 671 of file estimators.hpp.

SetFaceCoefficientFunction()

void mfem::KellyErrorEstimator::SetFaceCoefficientFunction ( FaceCoefficientFunction  compute_face_coefficient_ )

inline

Change the method to compute hₖ on a per-element basis.

Parameters

compute_face_coefficient_

A function taking a mesh and a face index to compute the local hₖ for the face.

Definition at line 682 of file estimators.hpp.

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

• fem/estimators.hpp
• fem/estimators.cpp