A posteriori error estimates for the 3 D stabilized Mortar finite element method applied to the Laplace equation

Zakaria Belhachmi

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2003)

  • Volume: 37, Issue: 6, page 991-1011
  • ISSN: 0764-583X

Abstract

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We consider a non-conforming stabilized domain decomposition technique for the discretization of the three-dimensional Laplace equation. The aim is to extend the numerical analysis of residual error indicators to this model problem. Two formulations of the problem are considered and the error estimators are studied for both. In the first one, the error estimator provides upper and lower bounds for the energy norm of the mortar finite element solution whereas in the second case, it also estimates the error for the Lagrange multiplier.

How to cite

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Belhachmi, Zakaria. "A posteriori error estimates for the $3$D stabilized Mortar finite element method applied to the Laplace equation." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 37.6 (2003): 991-1011. <http://eudml.org/doc/244949>.

@article{Belhachmi2003,
abstract = {We consider a non-conforming stabilized domain decomposition technique for the discretization of the three-dimensional Laplace equation. The aim is to extend the numerical analysis of residual error indicators to this model problem. Two formulations of the problem are considered and the error estimators are studied for both. In the first one, the error estimator provides upper and lower bounds for the energy norm of the mortar finite element solution whereas in the second case, it also estimates the error for the Lagrange multiplier.},
author = {Belhachmi, Zakaria},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Mortar finite element method; a posteriori estimates; mixed variational formulation; stabilization technique; non-matching grids; error estimate; mortar finite element method; Laplace equation; decomposition techniques; stability},
language = {eng},
number = {6},
pages = {991-1011},
publisher = {EDP-Sciences},
title = {A posteriori error estimates for the $3$D stabilized Mortar finite element method applied to the Laplace equation},
url = {http://eudml.org/doc/244949},
volume = {37},
year = {2003},
}

TY - JOUR
AU - Belhachmi, Zakaria
TI - A posteriori error estimates for the $3$D stabilized Mortar finite element method applied to the Laplace equation
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2003
PB - EDP-Sciences
VL - 37
IS - 6
SP - 991
EP - 1011
AB - We consider a non-conforming stabilized domain decomposition technique for the discretization of the three-dimensional Laplace equation. The aim is to extend the numerical analysis of residual error indicators to this model problem. Two formulations of the problem are considered and the error estimators are studied for both. In the first one, the error estimator provides upper and lower bounds for the energy norm of the mortar finite element solution whereas in the second case, it also estimates the error for the Lagrange multiplier.
LA - eng
KW - Mortar finite element method; a posteriori estimates; mixed variational formulation; stabilization technique; non-matching grids; error estimate; mortar finite element method; Laplace equation; decomposition techniques; stability
UR - http://eudml.org/doc/244949
ER -

References

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  13. [13] R. Verfürth, Error estimates for some quasi-interpolation operators. Modél. Math. Anal. Numér. 33 (1999) 695–713. Zbl0938.65125
  14. [14] R. Verfürth, A Review of A posteriori Error Estimation and Adaptive Mesh-Refinement Techniques. Wiley & Teubner (1996). Zbl0853.65108
  15. [15] O.B. Widlund, An extention theorem for finite element spaces with three applications, in Numerical Techniques in Continuum Mechanics, Proceedings of the Second GAMM Seminar, W Hackbush, K. Witsch Eds., Kiel (1986). Zbl0615.65114
  16. [16] B. Wohlmuth, A residual based error estimator for mortar finite element discretization. Numer. Math. 84 (1999) 143–171. Zbl0962.65090

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