692	RWTH Publication No: 1009807        2025
TITLE	Adaptive stochastic Galerkin finite element methods: Optimality and non-affine coefficients
AUTHORS	Markus Bachmayr, Henrik Eisenmann, Igor Voulis
ABSTRACT	Near-optimal computational complexity of an adaptive stochastic Galerkin method with independently refined spatial meshes for elliptic partial differential equations is shown. The method takes advantage of multilevel structure in expansions of random diffusion coefficients and combines operator compression in the stochastic variables with error estimation using finite element frames in space. A new operator compression strategy is introduced for nonlinear coefficient expansions, such as diffusion coefficients with log-affine structure.
KEYWORDS	stochastic Galerkin method, finite elements, frame-based error estimation, multilevel expansions of random fields, optimality