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Abstract
A general adaptive refinement strategy for solving linear elliptic partial differential equation with random data is proposed and analysed herein. The adaptive strategy extends the a posteriori error estimation framework introduced by Guignard & Nobile in 2018 (SIAM J. Numer. Anal., 56, 3121-3143) to cover problems with a nonaffine parametric coefficient dependence. A suboptimal, but nonetheless reliable and convenient implementation of the strategy involves approximation of the decoupled PDE problems with a common finite element approximation space. Computational results obtained using such a single-level strategy are presented in this paper (part I). Results obtained using a potentially more efficient multilevel approximation strategy, where meshes are individually tailored, will be discussed in part II of this work. The codes used to generate the numerical results are available online.
Original language | English |
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Pages (from-to) | A3393-A3412 |
Number of pages | 20 |
Journal | SIAM Journal on Scientific Computing |
Volume | 44 |
Issue number | 5 |
Early online date | 20 Oct 2022 |
DOIs | |
Publication status | Published - Oct 2022 |
Keywords
- adaptivity
- error estimation
- PDEs with random data
- finite element approximation
- stochastic collocation
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Dive into the research topics of 'Error estimation and adaptivity for stochastic collocation finite elements. Part I: single-level approximation'. Together they form a unique fingerprint.Projects
- 2 Finished
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Adaptive multilevel stochastic collocation methods for uncertainty quantification
Engineering & Physical Science Research Council
1/12/21 → 30/11/22
Project: Research Councils
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Numerical analysis of adaptive UQ algorithms for PDEs with random inputs
Engineering & Physical Science Research Council
20/06/17 → 31/07/21
Project: Research Councils