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

• A posteriori global error estimator for reduced basis approximation.
• An error indicator that measures the error due the reduced basis approximation.
• An error indicator that measures the error due the finite element approximation.
• These errors are developed for a greedy algorithm.
• The global error and the reduced basis error are upper bound of the “exact” errors.

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.