A constitutive relation error estimator based on traction-free recovery of the equilibrated stress

Abstract : A new methodology for recovering equilibrated stress fields is presented, which is based on traction-free subdomains’ computations. It allows a rather simple implementation in a standard finite element code compared with the standard technique for recovering equilibrated tractions. These equilibrated stresses are used to compute a constitutive relation error estimator for a finite element model in 2D linear elasticity. A lower bound and an upper bound for the discretization error are derived from the error in the constitutive relation. These bounds in the discretization error are used to build lower and upper bounds for local quantities of interest.
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L. Gallimard. A constitutive relation error estimator based on traction-free recovery of the equilibrated stress. International Journal for Numerical Methods in Engineering, Wiley, 2009, 78 (4), pp.460 - 482. ⟨10.1002/nme.2496⟩. ⟨hal-01689801⟩

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