A posteriori error estimation and adaptive strategy for the control of MsFEM computations

Ludovic Chamoin (1, 2) , Frédéric Legoll (3, 2)

1 LMT - Laboratoire de Mécanique et Technologie
2 MATHERIALS - MATHematics for MatERIALS
3 NAVIER UMR 8205 - Laboratoire Navier

We introduce quantitative and robust tools to control the numerical accuracy in simulations performed using the Multiscale Finite Element Method (MsFEM). First, we propose a guaranteed and fully computable a posteriori error estimate for the global error measured in the energy norm. It is based on dual analysis and the Constitutive Relation Error (CRE) concept, with recovery of equilibrated fluxes from the approximate MsFEM solution. Second, the estimate is split into several indicators, associated to the various MsFEM error sources, in order to drive an adaptive procedure. The overall strategy thus enables to automatically identify an appropriate trade-off between accuracy and computational cost in the MsFEM numerical simulations. Furthermore, the strategy is compatible with the offline/online paradigm of MsFEM. The performances of our approach are demonstrated on several numerical experiments.

Mots clés: Adaptivity; Multiscale problems; MsFEM approach; A posteriori error estimation

Domaines: Analyse numérique [math.NA]; Mécanique des solides [physics.class-ph]

Ludovic Chamoin, Frédéric Legoll. A posteriori error estimation and adaptive strategy for the control of MsFEM computations. Computer Methods in Applied Mechanics and Engineering, 2018, 336, pp.1-38. ⟨10.1016/j.cma.2018.02.016⟩. ⟨hal-01586825⟩