A posteriori error estimates for a nonconforming finite element discretization of the heat equation

Serge Nicaise[1]; Nadir Soualem

  • [1] Université de Valenciennes et du Hainaut Cambrésis, MACS, Le Mont Houy, 59313 Valenciennes Cedex 9, France. http://www.univ-valenciennes.fr/macs/Serge.Nicaise

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2005)

  • Volume: 39, Issue: 2, page 319-348
  • ISSN: 0764-583X

Abstract

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The paper presents an a posteriori error estimator for a (piecewise linear) nonconforming finite element approximation of the heat equation in ℝ d , d = 2 or 3, using backward Euler’s scheme. For this discretization, we derive a residual indicator, which use a spatial residual indicator based on the jumps of normal and tangential derivatives of the nonconforming approximation and a time residual indicator based on the jump of broken gradients at each time step. Lower and upper bounds form the main results with minimal assumptions on the mesh. Numerical experiments and a space-time adaptive algorithm confirm the theoretical predictions.

How to cite

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Nicaise, Serge, and Soualem, Nadir. "A posteriori error estimates for a nonconforming finite element discretization of the heat equation." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 39.2 (2005): 319-348. <http://eudml.org/doc/245732>.

@article{Nicaise2005,
abstract = {The paper presents an a posteriori error estimator for a (piecewise linear) nonconforming finite element approximation of the heat equation in $\mathbb \{R\}^d$, $d=2$ or 3, using backward Euler’s scheme. For this discretization, we derive a residual indicator, which use a spatial residual indicator based on the jumps of normal and tangential derivatives of the nonconforming approximation and a time residual indicator based on the jump of broken gradients at each time step. Lower and upper bounds form the main results with minimal assumptions on the mesh. Numerical experiments and a space-time adaptive algorithm confirm the theoretical predictions.},
affiliation = {Université de Valenciennes et du Hainaut Cambrésis, MACS, Le Mont Houy, 59313 Valenciennes Cedex 9, France. http://www.univ-valenciennes.fr/macs/Serge.Nicaise},
author = {Nicaise, Serge, Soualem, Nadir},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {error estimator; nonconforming FEM; heat equation; nonconforming finite element; backward Euler's scheme; numerical experiments; space-time adaptive algorithm},
language = {eng},
number = {2},
pages = {319-348},
publisher = {EDP-Sciences},
title = {A posteriori error estimates for a nonconforming finite element discretization of the heat equation},
url = {http://eudml.org/doc/245732},
volume = {39},
year = {2005},
}

TY - JOUR
AU - Nicaise, Serge
AU - Soualem, Nadir
TI - A posteriori error estimates for a nonconforming finite element discretization of the heat equation
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2005
PB - EDP-Sciences
VL - 39
IS - 2
SP - 319
EP - 348
AB - The paper presents an a posteriori error estimator for a (piecewise linear) nonconforming finite element approximation of the heat equation in $\mathbb {R}^d$, $d=2$ or 3, using backward Euler’s scheme. For this discretization, we derive a residual indicator, which use a spatial residual indicator based on the jumps of normal and tangential derivatives of the nonconforming approximation and a time residual indicator based on the jump of broken gradients at each time step. Lower and upper bounds form the main results with minimal assumptions on the mesh. Numerical experiments and a space-time adaptive algorithm confirm the theoretical predictions.
LA - eng
KW - error estimator; nonconforming FEM; heat equation; nonconforming finite element; backward Euler's scheme; numerical experiments; space-time adaptive algorithm
UR - http://eudml.org/doc/245732
ER -

References

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