On the convergence of adaptive stochastic collocation for elliptic partial differential equations with affine diffusion
Convergence of an adaptive collocation method for the parametric stationary diffusion
equation with finite-dimensional affine coefficient is shown. The adaptive algorithm relies on …
equation with finite-dimensional affine coefficient is shown. The adaptive algorithm relies on …
Convergence of adaptive stochastic Galerkin FEM
We propose and analyze novel adaptive algorithms for the numerical solution of elliptic
partial differential equations with parametric uncertainty. Four different marking strategies …
partial differential equations with parametric uncertainty. Four different marking strategies …
Adaptive stochastic Galerkin FEM for lognormal coefficients in hierarchical tensor representations
Stochastic Galerkin methods for non-affine coefficient representations are known to cause
major difficulties from theoretical and numerical points of view. In this work, an adaptive …
major difficulties from theoretical and numerical points of view. In this work, an adaptive …
Error estimation and adaptivity for stochastic collocation finite elements part I: single-level approximation
A general adaptive refinement strategy for solving linear elliptic partial differential equations
with random data is proposed and analysed herein. The adaptive strategy extends the a …
with random data is proposed and analysed herein. The adaptive strategy extends the a …
Error estimation and adaptivity for stochastic collocation finite elements Part II: multilevel approximation
A Bespalov, D Silvester - SIAM Journal on Scientific Computing, 2023 - SIAM
A multilevel adaptive refinement strategy for solving linear elliptic partial differential
equations with random data is recalled in this work. The strategy extends the a posteriori …
equations with random data is recalled in this work. The strategy extends the a posteriori …
T-IFISS: a toolbox for adaptive FEM computation
T-IFISS is a finite element software package for studying finite element solution algorithms
for deterministic and parametric elliptic partial differential equations. The emphasis is on self …
for deterministic and parametric elliptic partial differential equations. The emphasis is on self …
Convergence and rate optimality of adaptive multilevel stochastic Galerkin FEM
A Bespalov, D Praetorius… - IMA Journal of Numerical …, 2022 - academic.oup.com
We analyze an adaptive algorithm for the numerical solution of parametric elliptic partial
differential equations in two-dimensional physical domains, with coefficients and right-hand …
differential equations in two-dimensional physical domains, with coefficients and right-hand …
An adaptive stochastic Galerkin method based on multilevel expansions of random fields: Convergence and optimality
M Bachmayr, I Voulis - ESAIM: Mathematical Modelling and …, 2022 - esaim-m2an.org
The subject of this work is a new stochastic Galerkin method for second-order elliptic partial
differential equations with random diffusion coefficients. It combines operator compression in …
differential equations with random diffusion coefficients. It combines operator compression in …
Two-level a posteriori error estimation for adaptive multilevel stochastic Galerkin finite element method
The paper considers a class of parametric elliptic partial differential equations (PDEs),
where the coefficients and the right-hand side function depend on infinitely many (uncertain) …
where the coefficients and the right-hand side function depend on infinitely many (uncertain) …
Dynamical low rank approximation for uncertainty quantification of time-dependent problems
E Vidlicková - 2022 - infoscience.epfl.ch
The quantification of uncertainties can be particularly challenging for problems requiring
long-time integration as the structure of the random solution might considerably change over …
long-time integration as the structure of the random solution might considerably change over …