Adaptive Basis Enrichment for the Reduced Basis Method Applied to Finite Volume Schemes

We derive an efficient reduced basis method for finite volume approximations of parameterized linear advection-diffusion equations. An important step in deriving a reduced finite volume model with the reduced basis technology is the generation of a reduced basis space, on which the detailed numerical simulations are projected. We present a new strategy for this reduced basis generation. We apply an effective exploration of the parameter space by adaptive grids based on an a posteriori error estimate. The resulting method gives a considerable improvement concerning equal distribution of the model error over the parameter space compared to uniform parameter selections. It is computationally very efficient in terms of small ratio of training-time over model-error.