A Weighted Reduced Basis Method for Elliptic Partial Differential Equations with Random Input Data

08/2013

A Weighted Reduced Basis Method for Elliptic Partial Differential Equations with Random Input Data

Friday 22nd February 2013

Chen, P.; Quarteroni, A.; Rozza, G.

In this work we propose and analyze a weighted reduced basis method to solve elliptic partial differential equation (PDE) with random input data. The PDE is first transformed into a weighted parametric elliptic problem depending on a finite number of parameters. Distinctive importance at different values of the parameters are taken into account by assigning different weight to the samples in the greedy sampling procedure. A priori convergence analysis is carried out by constructive approximation of the exact solution with respect to the weighted parameters. Numerical examples are provided for the assessment of the advantages of the proposed method over the reduced basis method and stochastic collocation method in both univariate and multivariate stochastic problems. Keywords: weighted reduced basis method, stochastic partial differential equation, uncertainty quantication, stochastic collocation method, Kolmogorov N-width, exponential convergence