Geodesic
A posteriori error estimates for a nonconforming finite element discretization of the heat equation
Nicaise, Serge1  ; Soualem, Nadir 
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 , Tome 39 (2005) no. 2, pp. 319-348

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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.

DOI : 10.1051/m2an:2005009
Classification : 65N15, 65N30, 65M50
Keywords: error estimator, nonconforming FEM, heat equation

Nicaise, Serge 1 ; Soualem, Nadir 

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 
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     title = {A posteriori error estimates for a nonconforming finite element discretization of the heat equation},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {319--348},
     publisher = {EDP-Sciences},
     volume = {39},
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     year = {2005},
     doi = {10.1051/m2an:2005009},
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Nicaise, Serge; Soualem, Nadir. A posteriori error estimates for a nonconforming finite element discretization of the heat equation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 39 (2005) no. 2, pp. 319-348. doi: 10.1051/m2an:2005009

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