Roman Andreev

Sparse Tensor Discretization of Elliptic sPDEs

We propose and analyze sparse deterministic-stochastic tensor Galerkin finite element methods (sparse sGFEMs) for the numerical solution of elliptic partial differential equations (PDEs) with random coefficients in a physical domain

Multilevel preconditioning and low rank tensor iteration for space-time simultaneous discretizations of parabolic PDES

D\subset\mathbb{R}^d

Generalized Convergence Rates Results for Linear Inverse Problems in Hilbert Spaces

. In tensor product sGFEMs, the variational solution to the boundary value problem is approximated in tensor product finite element spaces

Space-time discretization of the heat equation

V^\Gamma\otimes V^D

Kolmogorov-Chentsov Theorem and Differentiability of Random Fields on Manifolds

, where

Sparse tensor approximation of parametric eigenvalue problems

V^\Gamma

Optimality of adaptive Galerkin methods for random parabolic partial differential equations

and

Convergence Rates of Sparse Tensor GPC FEM for Elliptic sPDEs

V^D

Preconditioning the augmented Lagrangian method for instationary mean field games with diffusion

denote suitable finite dimensional subspaces of the stochastic and deterministic function spaces, respectively. These approaches lead to sGFEM algorithms of complexity

Tikhonov and Landweber convergence rates: characterization by interpolation spaces

O(N_\Gamma N_D)