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 …
Efficient adaptive multilevel stochastic Galerkin approximation using implicit a posteriori error estimation
Partial differential equations (PDEs) with inputs that depend on infinitely many parameters
pose serious theoretical and computational challenges. Sophisticated numerical algorithms …
pose serious theoretical and computational challenges. Sophisticated numerical algorithms …
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 …
Goal-oriented error estimation and adaptivity for elliptic PDEs with parametric or uncertain inputs
We use the ideas of goal-oriented error estimation and adaptivity to design and implement
an efficient adaptive algorithm for approximating linear quantities of interest derived from …
an efficient adaptive algorithm for approximating linear quantities of interest derived from …
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 …
A fully adaptive multilevel stochastic collocation strategy for solving elliptic PDEs with random data
We propose and analyse a fully adaptive strategy for solving elliptic PDEs with random data
in this work. A hierarchical sequence of adaptive mesh refinements for the spatial …
in this work. A hierarchical sequence of adaptive mesh refinements for the spatial …
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 …
Efficient adaptive algorithms for elliptic PDEs with random data
A Bespalov, L Rocchi - SIAM/ASA Journal on Uncertainty Quantification, 2018 - SIAM
We present a novel adaptive algorithm implementing the stochastic Galerkin finite element
method for numerical solution of elliptic PDE problems with correlated random data. The …
method for numerical solution of elliptic PDE problems with correlated random data. The …