A posteriori global error estimator based on the error in the constitutive relation for reduced basis approximation of parametrized linear elastic problems

Abstract : In this paper we introduce a posteriori error estimator based on the concept of error in the constitutive relation to verify parametric models computed with a reduced basis approximation. We develop a global error estimator which leads to an upper bound for the exact error and takes into account all the error sources: the error due to the reduced basis approximation as well as the error due to the finite element approximation. We propose an error indicator to measure the quality of the reduced basis approximation and we deduce an error indicator on the finite element approximation.
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Laurent Gallimard, David Ryckelynck. A posteriori global error estimator based on the error in the constitutive relation for reduced basis approximation of parametrized linear elastic problems. Applied Mathematical Modelling, Elsevier, 2016, 40, pp.4271-4284. ⟨10.1016/j.apm.2015.11.016⟩. ⟨hal-01305736⟩

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