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

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

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

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topNicaise, 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 -

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