This work presents an h p-adaptive variant of multi-element polynomial chaos expansion
(ME-gPCE), referred to as anisotropic multi-element polynomial chaos expansion (AME-
gPCE). The main advantage of the proposed framework is that the basis functions of the
local gPCE are selected adaptively within each local element. The p-adaptivity allows the
order of the local uni-variate polynomials to be increased only for the dimensions associated
with highly non-linear behaviour of the response surface, while the h-adaptivity allows the …