Stochastic Galerkin reduced basis methods for parametrized random elliptic PDEs

We consider the estimation of parameter-dependent statistical outputs for parametrized elliptic PDE problems with random data. We propose a stochastic Galerkin reduced basis method, which provides the expected output for a given parameter value at the cost of solving a single low-dimensional system of equations. This is substantially faster than usual Monte Carlo reduced basis methods, which require multiple samples of the reduced solution.