Direct and Inverse Problems for PDEs with Random Coefficients - Abstract
In this talk, we provide regularity results for the solution to elliptic diffusion problems on random domains. Especially, based on the decay of the Karhunen-Loeve expansion of the domain perturbation field, we establish rates of decay which are feasible for several numerical quadrature methods. We moreover employ parametric finite elements to compute the solution of the diffusion problem on each particular realization of the domain generated by the perturbation field. This simplifies the implementation and yields a non-intrusive approach. The theoretical findings are complemented by numerical examples.