Residual and hierarchical a posteriori error estimates for nonconforming mixed finite element methods

Linda El Alaoui; Alexandre Ern

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 38, Issue: 6, page 903-929
  • ISSN: 0764-583X

Abstract

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We analyze residual and hierarchical a posteriori error estimates for nonconforming finite element approximations of elliptic problems with variable coefficients. We consider a finite volume box scheme equivalent to a nonconforming mixed finite element method in a Petrov–Galerkin setting. We prove that all the estimators yield global upper and local lower bounds for the discretization error. Finally, we present results illustrating the efficiency of the estimators, for instance, in the simulation of Darcy flows through heterogeneous porous media.

How to cite

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El Alaoui, Linda, and Ern, Alexandre. "Residual and hierarchical a posteriori error estimates for nonconforming mixed finite element methods." ESAIM: Mathematical Modelling and Numerical Analysis 38.6 (2010): 903-929. <http://eudml.org/doc/194249>.

@article{ElAlaoui2010,
abstract = { We analyze residual and hierarchical a posteriori error estimates for nonconforming finite element approximations of elliptic problems with variable coefficients. We consider a finite volume box scheme equivalent to a nonconforming mixed finite element method in a Petrov–Galerkin setting. We prove that all the estimators yield global upper and local lower bounds for the discretization error. Finally, we present results illustrating the efficiency of the estimators, for instance, in the simulation of Darcy flows through heterogeneous porous media. },
author = {El Alaoui, Linda, Ern, Alexandre},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Finite elements; nonconforming methods; a posteriori error estimates; finite volumes; Darcy equations; heterogeneous media.; finite elements; nonconforming methods, a posteriori error estimates; heterogeneous media; elliptic problems; numerical results; Darcy flows; porous media},
language = {eng},
month = {3},
number = {6},
pages = {903-929},
publisher = {EDP Sciences},
title = {Residual and hierarchical a posteriori error estimates for nonconforming mixed finite element methods},
url = {http://eudml.org/doc/194249},
volume = {38},
year = {2010},
}

TY - JOUR
AU - El Alaoui, Linda
AU - Ern, Alexandre
TI - Residual and hierarchical a posteriori error estimates for nonconforming mixed finite element methods
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 38
IS - 6
SP - 903
EP - 929
AB - We analyze residual and hierarchical a posteriori error estimates for nonconforming finite element approximations of elliptic problems with variable coefficients. We consider a finite volume box scheme equivalent to a nonconforming mixed finite element method in a Petrov–Galerkin setting. We prove that all the estimators yield global upper and local lower bounds for the discretization error. Finally, we present results illustrating the efficiency of the estimators, for instance, in the simulation of Darcy flows through heterogeneous porous media.
LA - eng
KW - Finite elements; nonconforming methods; a posteriori error estimates; finite volumes; Darcy equations; heterogeneous media.; finite elements; nonconforming methods, a posteriori error estimates; heterogeneous media; elliptic problems; numerical results; Darcy flows; porous media
UR - http://eudml.org/doc/194249
ER -

References

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