Equilibrated stress reconstructions for linear elasticity problems with application to a posteriori error analysis

Rita Riedlbeck (1, 2) , Daniele Di Pietro (1) , Alexandre Ern (3, 4)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 IMSIA - UMR 9219 - Institut des Sciences de la mécanique et Applications industrielles
3 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
4 SERENA - Simulation for the Environment: Reliable and Efficient Numerical Algorithms

We present an a posteriori error estimate for the linear elasticity problem. The estimate is based on an equilibrated reconstruction of the Cauchy stress tensor, which is obtained from mixed finite element solutions of local Neumann problems. We propose two different reconstructions, one using Arnold–Winther mixed finite element spaces providing a symmetric stress tensor and one using Arnold–Falk– Winther mixed finite element spaces with a weak symmetry constraint. The performance of the estimate is illustrated on a numerical test with analytical solution.

Mots clés: Arnold–Falk–Winther finite element; linear elasticity; a posteriori error estimate; Arnold–Winther finite element; equilibrated stress reconstruction

Domaines: Analyse numérique [math.NA]

Rita Riedlbeck, Daniele Di Pietro, Alexandre Ern. Equilibrated stress reconstructions for linear elasticity problems with application to a posteriori error analysis. Clément Cancès; Pascal Omnes. Finite Volumes for Complex Applications VIII – Methods and Theoretical Aspects, 199, pp.293-301, 2017, Springer Proceedings in Mathematics & Statistics, 978-3-319-57397-7. ⟨10.1007/978-3-319-57397-7⟩. ⟨hal-01433841v2⟩