Evaluation of Flux Integral Outputs for the Reduced Basis Method

In this paper, we consider the evaluation of flux integral outputs from reduced basis solutions to second-order PDEs. In order to evaluate such outputs, a lifting function v ⋆ must be chosen. In the standard finite element context, this choice is not relevant, whereas in the reduced basis context, as we show, it greatly affects the output error. We propose two "good" choices for v ⋆ and illustrate their effect on the output error by examining a numerical example. We also make clear the role of v ⋆ in a more general primal-dual reduced basis approximation framework.