A new Hierarchical Model Reduction-Reduced Basis technique for advection-diffusion-reaction problems

Ohlberger M, Smetana K

Abstract

We extend previous work on the Hierarchical Model Reduction-Reduced Basis (HMR-RB) approach to an advection-diffusion-reaction problem. In comparison to the Boussinesq approach we do not neglect the dependency on the vertical direction but enhance the solution for the horizontal direction with appropriately chosen basis functions living on the vertical one. This is done by a combination of the frameworks of hierarchical model reduction and the reduced basis methods. We derive a new a posteriori error estimate and demonstrate in numerical experiments that few basis functions suffice to get good approximations.