Sparse second moment analysis for elliptic problems in stochastic domains
The authors consider the Dirichlet problem for the Poisson equation \[ -\Delta u_{\varepsilon}(\omega)=f\text{ in\;}D_{\varepsilon}(\omega ),\;u_{\varepsilon}(\omega)=g\text{ on }\partial D_{\varepsilon}(\omega), \] where \(D_{\varepsilon}(\omega)\) is a small random perturbation of a domain \(D\subset\mathbb{R}^{n},\;n=2,3.\) They develop a deterministic second moment analysis of the random solution and propose a fast wavelet based algorithm to approximate its mean and correlation function. Some numerical experiments are presented.
scientific article; zbMATH DE number 5288752
scientific article