Convergence analysis of the adaptive stochastic collocation finite element method
| Title: | Convergence analysis of the adaptive stochastic collocation finite element method |
|---|---|
| Authors: | Bespalov, Alex, Savinov, Andrey |
| Publication Year: | 2024 |
| Collection: | Computer Science Mathematics |
| Subject Terms: | Mathematics - Numerical Analysis, Mathematics - Analysis of PDEs |
| More Details: | This paper is focused on the convergence analysis of an adaptive stochastic collocation algorithm for the stationary diffusion equation with parametric coefficient. The algorithm employs sparse grid collocation in the parameter domain alongside finite element approximations in the spatial domain, and adaptivity is driven by recently proposed parametric and spatial a posteriori error indicators. We prove that for a general diffusion coefficient with finite-dimensional parametrization, the algorithm drives the underlying error estimates to zero. Thus, our analysis covers problems with affine and nonaffine parametric coefficient dependence. Comment: 26 pages, 6 figures |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/2401.14894 |
| Accession Number: | edsarx.2401.14894 |
| Database: | arXiv |
| Description not available. |