{Reference Type}: Journal Article
{Title}: A stochastic collocation approach for parabolic PDEs with random domain deformations.
{Author}: Castrillón-Candás JE;Xu J;
{Journal}: Comput Math Appl
{Volume}: 93
{Issue}: 0
{Year}: Jul 2021 1
{Factor}: 3.218
{DOI}: 10.1016/j.camwa.2021.04.005
{Abstract}: 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.