mfem::LSZienkiewiczZhuEstimator Class Reference

The LSZienkiewiczZhuEstimator class implements the Zienkiewicz-Zhu error estimation procedure [1,2] using face-based patches [3]. More...

#include <estimators.hpp>

Inheritance diagram for mfem::LSZienkiewiczZhuEstimator:

Collaboration diagram for mfem::LSZienkiewiczZhuEstimator:

Public Member Functions
	LSZienkiewiczZhuEstimator (BilinearFormIntegrator &integ, GridFunction &sol)
	Construct a new LSZienkiewiczZhuEstimator object. More...
void	SetWithCoeff (bool w_coeff=true)
	Consider the coefficient in BilinearFormIntegrator to calculate the fluxes for the error estimator. More...
void	DisableReconstructionAcrossSubdomains ()
	Disable reconstructing the flux in patches spanning different subdomains. More...
void	SetTichonovRegularization (double tcoeff=1.0e-8)
	Solve a Tichonov-regularized least-squares problem for the reconstructed fluxes. This is especially helpful for when not using tensor product elements, which typically require fewer integration points and, therefore, may lead to an ill-conditioned linear system. More...
virtual double	GetTotalError () const override
	Return the total error from the last error estimate. More...
virtual const Vector &	GetLocalErrors () override
	Get a Vector with all element errors. More...
virtual void	Reset () override
	Reset the error estimator. More...
virtual	~LSZienkiewiczZhuEstimator ()
Public Member Functions inherited from mfem::ErrorEstimator
virtual	~ErrorEstimator ()
	Destruct the error estimator. More...
Public Member Functions inherited from mfem::AbstractErrorEstimator
virtual	~AbstractErrorEstimator ()

Protected Member Functions
bool	MeshIsModified ()
	Check if the mesh of the solution was modified. More...
void	ComputeEstimates ()
	Compute the element error estimates. More...

Protected Attributes
long	current_sequence
Vector	error_estimates
double	total_error
bool	subdomain_reconstruction = true
double	tichonov_coeff
BilinearFormIntegrator &	integ
GridFunction &	solution
bool	with_coeff

Detailed Description

The LSZienkiewiczZhuEstimator class implements the Zienkiewicz-Zhu error estimation procedure [1,2] using face-based patches [3].

[1] Zienkiewicz, O.C. and Zhu, J.Z., The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique. Int. J. Num. Meth. Engng. 33, 1331-1364 (1992).

[2] Zienkiewicz, O.C. and Zhu, J.Z., The superconvergent patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity. Int. J. Num. Meth. Engng. 33, 1365-1382 (1992).

[3] Bartels, S. and Carstensen, C., Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. Part II: Higher order FEM. Math. Comp. 71(239), 971-994 (2002)

The required BilinearFormIntegrator must implement the method ComputeElementFlux().

COMMENTS: The present implementation ignores all single-element patches corresponding to boundary faces. This is appropriate for Dirichlet boundaries, but suboptimal for Neumann boundaries. Reference 3 shows that a constrained least-squares problem, where the reconstructed flux is constrained by the Neumann boundary data, is appropriate to handle this case. NOTE THAT THIS CONSTRAINED LS PROBLEM IS NOT YET IMPLEMENTED, so it is possible that the local error estimates for elements on a Neumann boundary are suboptimal. The global polynomial basis used for the flux reconstruction is, by default, aligned with the physical Cartesian axis. For patches with 2D elements, this has been improved on so that the basis is aligned with the physical patch orientation. Reorientation of the flux reconstruction basis is helpful to maintain symmetry in the refinement pattern and could be extended to 3D. This estimator is ONLY implemented IN SERIAL. Anisotropic refinement is NOT YET SUPPORTED.

Definition at line 241 of file estimators.hpp.

Constructor & Destructor Documentation

mfem::LSZienkiewiczZhuEstimator::LSZienkiewiczZhuEstimator ( BilinearFormIntegrator &  integ, GridFunction &  sol  )

inline

Construct a new LSZienkiewiczZhuEstimator object.

Parameters

integ	This BilinearFormIntegrator must implement only the method ComputeElementFlux().
sol	The solution field whose error is to be estimated.

Definition at line 271 of file estimators.hpp.

virtual mfem::LSZienkiewiczZhuEstimator::~LSZienkiewiczZhuEstimator ( )

inlinevirtual

Definition at line 313 of file estimators.hpp.

Member Function Documentation

void mfem::LSZienkiewiczZhuEstimator::ComputeEstimates ( )

protected

Compute the element error estimates.

Definition at line 33 of file estimators.cpp.

void mfem::LSZienkiewiczZhuEstimator::DisableReconstructionAcrossSubdomains ( )

inline

Disable reconstructing the flux in patches spanning different subdomains.

Definition at line 287 of file estimators.hpp.

virtual const Vector& mfem::LSZienkiewiczZhuEstimator::GetLocalErrors ( )

inlineoverridevirtual

Get a Vector with all element errors.

Implements mfem::ErrorEstimator.

Definition at line 304 of file estimators.hpp.

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

inlineoverridevirtual

Return the total error from the last error estimate.

Reimplemented from mfem::ErrorEstimator.

Definition at line 301 of file estimators.hpp.

bool mfem::LSZienkiewiczZhuEstimator::MeshIsModified ( )

inlineprotected

Check if the mesh of the solution was modified.

Definition at line 255 of file estimators.hpp.

virtual void mfem::LSZienkiewiczZhuEstimator::Reset ( )

inlineoverridevirtual

Reset the error estimator.

Implements mfem::ErrorEstimator.

Definition at line 311 of file estimators.hpp.

void mfem::LSZienkiewiczZhuEstimator::SetTichonovRegularization ( double  tcoeff = 1.0e-8 )

inline

Solve a Tichonov-regularized least-squares problem for the reconstructed fluxes. This is especially helpful for when not using tensor product elements, which typically require fewer integration points and, therefore, may lead to an ill-conditioned linear system.

Definition at line 294 of file estimators.hpp.

void mfem::LSZienkiewiczZhuEstimator::SetWithCoeff ( bool  w_coeff = true )

inline

Consider the coefficient in BilinearFormIntegrator to calculate the fluxes for the error estimator.

Definition at line 283 of file estimators.hpp.

Member Data Documentation

long mfem::LSZienkiewiczZhuEstimator::current_sequence

protected

Definition at line 244 of file estimators.hpp.

Vector mfem::LSZienkiewiczZhuEstimator::error_estimates

protected

Definition at line 245 of file estimators.hpp.

BilinearFormIntegrator& mfem::LSZienkiewiczZhuEstimator::integ

protected

Definition at line 250 of file estimators.hpp.

GridFunction& mfem::LSZienkiewiczZhuEstimator::solution

protected

Definition at line 251 of file estimators.hpp.

bool mfem::LSZienkiewiczZhuEstimator::subdomain_reconstruction = true

protected

Definition at line 247 of file estimators.hpp.

double mfem::LSZienkiewiczZhuEstimator::tichonov_coeff

protected

Definition at line 248 of file estimators.hpp.

double mfem::LSZienkiewiczZhuEstimator::total_error

protected

Definition at line 246 of file estimators.hpp.

bool mfem::LSZienkiewiczZhuEstimator::with_coeff

protected

Definition at line 252 of file estimators.hpp.

---

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

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