Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs (Q2836463)

From the authors' abstract: The paper considers a model class of second-order, linear, parametric, elliptic partial differential equations (PDEs) on a bounded domain \(D\) with diffusion coefficients depending on the parameter vector \(y\). For such models, the entire family of solutions can be simultaneously approximated by multivariate sparse polynomials in the parameter \(y\). The paper presents an adaptive numerical algorithm for constructing a sequence of sparse polynomials that is proved to converge toward the solution. Numerical experiments are presented in large parameter dimension, which confirm the effectiveness of the adaptive approach.