Strict error bounds for linear solid mechanics problems using a subdomain-based flux-free method

Régis Cottereau (1) , Pedro Diez (2) , Antonio Huerta (2, 3)

1 MSSMat - Laboratoire de mécanique des sols, structures et matériaux
2 LaCàN - Laboratori de Càlcul Numèric (LACAN)
3 Departament de Matematica Aplicada III [Barcelona]

We discuss, in this paper, a flux-free method for the computation of strict upper bounds of the energy norm of the error in a Finite Element (FE) computation. The bounds are strict in the sense that they refer to the difference between the displacement computed on the FE mesh and the exact displacement, solution of the continuous equations, rather than to the difference between the displacements computed on two FE meshes, one coarse and one refined. This method is based on the resolution of a series of local problems on patches of elements and does not require the resolution of a previous problem of flux equilibration, as happens with other methods. The paper concentrates more specifically on linear solid mechanics issues, and on the assessment of the energy norm of the error, seen as a necessary tool for the estimation of the error in arbitrary quantities of interest (linear functional outputs). Applications in both 2D and 3D are presented.

Keywords: erification; A posteriori error estimation; Error bounds; Residual-based estimators; Flux-free error estimator

Domains: Physics [physics]; Mechanics [physics]; Mechanics of materials [physics.class-ph]; Engineering Sciences [physics]; Mechanics [physics.med-ph]; Mechanics of materials [physics.class-ph]

Régis Cottereau, Pedro Diez, Antonio Huerta. Strict error bounds for linear solid mechanics problems using a subdomain-based flux-free method. Computational Mechanics, 2009, 44 (4), pp.533-547. ⟨10.1007/s00466-009-0388-1⟩. ⟨hal-00707098⟩