Implicit a posteriori error estimation using patch recovery techniques

Tamás Horváth; Ferenc Izsák

Open Mathematics (2012)

  • Volume: 10, Issue: 1, page 55-72
  • ISSN: 2391-5455

Abstract

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We develop implicit a posteriori error estimators for elliptic boundary value problems. Local problems are formulated for the error and the corresponding Neumann type boundary conditions are approximated using a new family of gradient averaging procedures. Convergence properties of the implicit error estimator are discussed independently of residual type error estimators, and this gives a freedom in the choice of boundary conditions. General assumptions are elaborated for the gradient averaging which define a family of implicit a posteriori error estimators. We will demonstrate the performance and the favor of the method through numerical experiments.

How to cite

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Tamás Horváth, and Ferenc Izsák. "Implicit a posteriori error estimation using patch recovery techniques." Open Mathematics 10.1 (2012): 55-72. <http://eudml.org/doc/269098>.

@article{TamásHorváth2012,
abstract = {We develop implicit a posteriori error estimators for elliptic boundary value problems. Local problems are formulated for the error and the corresponding Neumann type boundary conditions are approximated using a new family of gradient averaging procedures. Convergence properties of the implicit error estimator are discussed independently of residual type error estimators, and this gives a freedom in the choice of boundary conditions. General assumptions are elaborated for the gradient averaging which define a family of implicit a posteriori error estimators. We will demonstrate the performance and the favor of the method through numerical experiments.},
author = {Tamás Horváth, Ferenc Izsák},
journal = {Open Mathematics},
keywords = {Implicit a posteriori error estimation; Finite element method; Gradient recovery; implicit a posteriori error estimators; finite element method; gradient recovery; elliptic boundary value problem; convergence; numerical examples},
language = {eng},
number = {1},
pages = {55-72},
title = {Implicit a posteriori error estimation using patch recovery techniques},
url = {http://eudml.org/doc/269098},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Tamás Horváth
AU - Ferenc Izsák
TI - Implicit a posteriori error estimation using patch recovery techniques
JO - Open Mathematics
PY - 2012
VL - 10
IS - 1
SP - 55
EP - 72
AB - We develop implicit a posteriori error estimators for elliptic boundary value problems. Local problems are formulated for the error and the corresponding Neumann type boundary conditions are approximated using a new family of gradient averaging procedures. Convergence properties of the implicit error estimator are discussed independently of residual type error estimators, and this gives a freedom in the choice of boundary conditions. General assumptions are elaborated for the gradient averaging which define a family of implicit a posteriori error estimators. We will demonstrate the performance and the favor of the method through numerical experiments.
LA - eng
KW - Implicit a posteriori error estimation; Finite element method; Gradient recovery; implicit a posteriori error estimators; finite element method; gradient recovery; elliptic boundary value problem; convergence; numerical examples
UR - http://eudml.org/doc/269098
ER -

References

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