A posteriori error estimates for a fully discrete approximation of Sobolev equations

Nicaise, Serge; Bekkouche, Fatiha

Confluentes Mathematici, Tome 11 (2019) no. 1, pp. 3-28.

The paper presents an a posteriori error estimator for a (piecewise linear) conforming finite element approximation of some (linear) Sobolev equations in ${ℝ}^d$, $d=2$ or 3, using implicit Euler’s scheme. For this discretization, we derive a residual indicator, which uses a spatial residual indicator based on the jumps of conormal derivatives of the approximations and a time residual indicator based on the jump (in an appropriated norm) of the successive solutions at each time step. Lower and upper bounds are obtained with minimal assumptions on the meshes. Numerical experiments that confirm and illustrate the theoretical results are given.

Classification : 65M15, 65M50, 65M60
Mots clés : Sobolev equations, a posteriori error analysis

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