Error estimates for inverse problems matching statistical moments in random elliptic PDEs

We propose an algorithm which allows for the optimal identification of statistical moments (mean value, variance, skewness, etc.) in elliptic PDEs with random coefficients, integrating the adjoint-based deterministic methods with a sparse grid stochastic collocation finite element approach.

We will present the existence results, characterization of optimal parameters, and some numerical examples showing the reduction in the number of simulations necessary for calibration. The error analysis is based on Fink-Rheinboldt’s results for parametrized nonlinear equations.