A posteriori error estimation for elliptic partial differential equations with small uncertainties (Q2804372)

The article is mainly concerned with diffusion problems \(-\text{div}(a\text{\,grad\,}u)= f\), where the coefficient \(a\) depends on a small uncertainty input expressed by finitely many random variables. The main goal is to compute bounds for the difference between the exact solution and some finite element approximation to the unperturbed problem in various norms. The approach is extended to some nonlinear problem class, and illustrated by some numerical examples.