A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data

In this paper we propose and analyze a stochastic collocation method to solve elliptic partial differential equations with random coefficients and forcing terms (input data of the model). The input data are assumed to depend on a finite number of random variables. The method consists in a Galerkin approximation in space and a collocation in the zeros of suitable tensor product orthogonal polynomials (Gauss points) in the probability space and naturally leads to the solution of uncoupled deterministic problems as in the Monte Carlo approach. It can be seen as a generalization of the stochastic Galerkin method proposed in [I. Babuška, R. Tempone, and G. E. Zouraris, SIAM J. Numer. Anal., 42 (2004), pp. 800–825]…

• UD
  U.S. Department of Energy

  Awards: FC52-08NA28615, DE-FC52-08NA28615
• KA
  King Abdullah University of Science and Technology
• PD
  Politecnico di Milano
• NN
  National Nuclear Security Administration

  Award: DE-FC52-08NA28615