A reduced basis method for fractional diffusion operators. I (Q2671267)

The authors propose and analyze a reduced basis method to evaluate fractional norms and apply fractional powers of elliptic operators. Their approach relies on several independent evaluations of \((I-t_i^2 \Delta )^{-1}f\) which can be computed in parallel way. Exponential rates of convergence for the optimal choice of sampling points \(t_i\) are proved. Several numerical experiments are provided to confirm the theoretical results.