Convergence analysis of the adaptive stochastic collocation finite element method
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910790665109504 |
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| author | Bespalov, Alex Savinov, Andrey |
| author_facet | Bespalov, Alex Savinov, Andrey |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14894 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergence analysis of the adaptive stochastic collocation finite element method Bespalov, Alex Savinov, Andrey Numerical Analysis Analysis of PDEs 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. |
| title | Convergence analysis of the adaptive stochastic collocation finite element method |
| topic | Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2401.14894 |