%0 Journal Article
%T A stochastic collocation approach for parabolic PDEs with random domain deformations.
%A Castrillón-Candás JE
%A Xu J
%J Comput Math Appl
%V 93
%N 0
%D Jul 2021 1
%M 34113061
%F 3.218
%R 10.1016/j.camwa.2021.04.005
%X In this article we analyze the linear parabolic partial differential equation with a stochastic domain deformation. In particular, we concentrate on the problem of numerically approximating the statistical moments of a given Quantity of Interest (QoI). The geometry is assumed to be random. The parabolic problem is remapped to a fixed deterministic domain with random coefficients and shown to admit an extension on a well defined region embedded in the complex hyperplane. The stochastic moments of the QoI are computed by employing a collocation method in conjunction with an isotropic Smolyak sparse grid. Theoretical sub-exponential convergence rates as a function to the number of collocation interpolation knots are derived. Numerical experiments are performed and they confirm the theoretical error estimates.