Convergence of adaptive stochastic collocation with finite elements

被引：8

作者：

Feischl, Michael ^{[1
]}

Scaglioni, Andrea ^{[1
]}

机构：

[1] TU Wien, Inst Anal & Sci Comp, Wiedner Hauptstr 8-10, A-1040 Vienna, Austria

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2021年 / 98卷 / 98期

基金：

奥地利科学基金会;

关键词：

Stochastic collocation; Adaptive mesh refinement; Uncertainty quantification; PARTIAL-DIFFERENTIAL-EQUATIONS; PETROV-GALERKIN DISCRETIZATION; POLYNOMIAL INTERPOLATION; UNCERTAINTY; APPROXIMATION;

D O I：

10.1016/j.camwa.2021.07.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider an elliptic partial differential equation with a random diffusion parameter discretized by a stochastic collocation method in the parameter domain and a finite element method in the spatial domain. We prove for the first time convergence of a stochastic collocation algorithm which adaptively enriches the parameter space as well as refines the finite element meshes.

引用

页码：139 / 156

页数：18

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