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

Serge Nicaise; Nadir Soualem

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • 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 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 39.2 (2010): 319-348. <http://eudml.org/doc/194264>.

@article{Nicaise2010,
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. },
author = {Nicaise, Serge, Soualem, Nadir},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Error estimator; nonconforming FEM; heat equation.; error estimator; nonconforming finite element; heat equation; backward Euler's scheme; numerical experiments; space-time adaptive algorithm},
language = {eng},
month = {3},
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/194264},
volume = {39},
year = {2010},
}

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
DA - 2010/3//
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.; error estimator; nonconforming finite element; heat equation; backward Euler's scheme; numerical experiments; space-time adaptive algorithm
UR - http://eudml.org/doc/194264
ER -

References

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