694	RWTH Publication No: 1013843        2025
TITLE	Sparse and low-rank approximations of parametric elliptic PDEs: the best of both worlds
AUTHORS	Markus Bachmayr, Huqing Yang
ABSTRACT	A new approximation format for solutions of partial differential equations de- pending on infinitely many parameters is introduced. By combining low-rank tensor approximation in a selected subset of variables with a sparse polynomial expansion in the remaining parametric variables, it addresses in particular classes of elliptic problems where a direct polynomial expansion is inefficient, such as those arising from random diffusion coefficients with short correlation length. A convergent adaptive solver is proposed and analyzed that maintains quasi-optimal ranks of approximations and at the same time yields optimal convergence rates of spatial discretizations without coarsening. The results are illustrated by numerical tests.
KEYWORDS	parametric elliptic PDEs, sparse polynomial approximations, low-rank tensor representations, adaptivity