**Donald Estep**

Department of Mathematics and Department of Statistics

Colorado State University

### Efficient Nonparametric Density Estimation for Randomly
Perturbed Elliptic Problems

We describe an efficient numerical method for nonparametric density estimation for quantities of interest computed from an elliptic problem with randomly perturbed parameters and data. The method employs the finite element method, non-overlapping domain decomposition, and the Neumann series for an invertible operator. We use an a posteriori error estimate using adjoint operators and variational analysis to distribute computational work in order to achieve a desired accuracy by an efficient distribution of computational resources.