Model reduction of semiaffinely parameterized partial differential equations by two-level affine approximation

We propose an improvement to the reduced basis method for parametric partial differential equations. An assumption of affine parameterization leads to an efficient offline-online decomposition when the problem is solved for many different parametric configurations. We consider an advection-diffusion problem, where the diffusive term is nonaffinely parameterized and treated with a two-level affine approximation given by the empirical interpolation method. The offline stage and a posteriori error estimation is performed using the coarse-level approximation, while the fine-level approximation is used to perform a correction iteration that reduces the actual error of the reduced basis approximation while keeping the same certified error bounds.