| Issue |
ESAIM: M2AN
Volume 39, Number 2, March-April 2005
|
|
|---|---|---|
| Page(s) | 319 - 348 | |
| DOI | https://doi.org/10.1051/m2an:2005009 | |
| Published online | 15 April 2005 | |
A posteriori error estimates for a nonconforming finite element discretization of the heat equation
Université de Valenciennes et du Hainaut Cambrésis,
MACS, ISTV,
59313 Valenciennes Cedex 9, France. Serge.Nicaise@univ-valenciennes.fr; Nadir.Soualem@univ-valenciennes.fr
Received:
12
July
2004
The paper presents an a posteriori error estimator for a (piecewise linear)
nonconforming finite element approximation of the heat equation
in 
, 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.
Mathematics Subject Classification: 65N15 / 65N30 / 65M50
Key words: Error estimator / nonconforming FEM / heat equation.
© EDP Sciences, SMAI, 2005
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