On the convergence of adaptive stochastic collocation for elliptic partial differential equations with affine diffusion

08/17/2020
by   Martin Eigel, et al.
0

Convergence of an adaptive collocation method for the stationary parametric diffusion equation with finite-dimensional affine coefficient is shown. The adaptive algorithm relies on a recently introduced residual-based reliable a posteriori error estimator. For the convergence proof, a strategy recently used for a stochastic Galerkin method with an hierarchical error estimator is transferred to the collocation setting. Extensions to other variants of adaptive collocation methods (including the classical one proposed in the paper "Dimension-adaptive tensor-product quadratuture" Computing (2003) by T. Gerstner and M. Griebel) is explored.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
06/11/2020

Truncation Preconditioners for Stochastic Galerkin Finite Element Discretizations

Stochastic Galerkin finite element method (SGFEM) provides an efficient ...
research
10/03/2019

Adaptive IGAFEM with optimal convergence rates: T-splines

We consider an adaptive algorithm for finite element methods for the iso...
research
02/06/2023

Convergence of adaptive Galerkin FEM for parametric PDEs with lognormal coefficients

Solving high-dimensional random parametric PDEs poses a challenging comp...
research
10/07/2022

Efficient Adaptive Stochastic Collocation Strategies for Advection-Diffusion Problems with Uncertain Inputs

Physical models with uncertain inputs are commonly represented as parame...
research
10/09/2019

Adaptive isogeometric analysis on two-dimensional trimmed domains based on a hierarchical approach

The focus of this work is on the development of an error-driven isogeome...
research
09/19/2021

An adaptive stochastic Galerkin method based on multilevel expansions of random fields: Convergence and optimality

The subject of this work is a new stochastic Galerkin method for second-...
research
09/15/2021

Error estimation and adaptivity for stochastic collocation finite elements Part I: single-level approximation

A general adaptive refinement strategy for solving linear elliptic parti...

Please sign up or login with your details

Forgot password? Click here to reset