01371nas a2200145   4500008004100000245010300041210006900144300001600213490000700229520080500236100001501041700002201056700002101078856012601099       2013                        eng d00aA weighted reduced basis method for elliptic partial differential equations with random input data0 aweighted reduced basis method for elliptic partial differential   a3163–31850 v513 aIn this work we propose and analyze a weighted reduced basis method to solve elliptic partial differential equations (PDEs) with random input data. The PDEs are first transformed into a weighted parametric elliptic problem depending on a finite number of parameters. Distinctive importance of the solution at different values of the parameters is taken into account by assigning different weights 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 the stochastic collocation method in both univariate and multivariate stochastic problems.1 aChen, Peng1 aQuarteroni, Alfio1 aRozza, Gianluigi  uhttps://math.sissa.it/publication/weighted-reduced-basis-method-elliptic-partial-differential-equations-random-input-data