MFEM
v4.5.2
Finite element discretization library
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The LSZienkiewiczZhuEstimator class implements the Zienkiewicz-Zhu error estimation procedure [1,2] using face-based patches [3]. More...
#include <estimators.hpp>
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 |
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.
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Construct a new LSZienkiewiczZhuEstimator object.
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.
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Definition at line 313 of file estimators.hpp.
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Compute the element error estimates.
Definition at line 33 of file estimators.cpp.
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Disable reconstructing the flux in patches spanning different subdomains.
Definition at line 287 of file estimators.hpp.
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Get a Vector with all element errors.
Implements mfem::ErrorEstimator.
Definition at line 304 of file estimators.hpp.
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Return the total error from the last error estimate.
Reimplemented from mfem::ErrorEstimator.
Definition at line 301 of file estimators.hpp.
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Check if the mesh of the solution was modified.
Definition at line 255 of file estimators.hpp.
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Reset the error estimator.
Implements mfem::ErrorEstimator.
Definition at line 311 of file estimators.hpp.
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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.
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Consider the coefficient in BilinearFormIntegrator to calculate the fluxes for the error estimator.
Definition at line 283 of file estimators.hpp.
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Definition at line 244 of file estimators.hpp.
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Definition at line 245 of file estimators.hpp.
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Definition at line 250 of file estimators.hpp.
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Definition at line 251 of file estimators.hpp.
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Definition at line 247 of file estimators.hpp.
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Definition at line 248 of file estimators.hpp.
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Definition at line 246 of file estimators.hpp.
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Definition at line 252 of file estimators.hpp.