On the Convergence of Adaptive Stochastic Collocation for Elliptic Partial Differential Equations with Affine Diffusion
| Autor: | Martin Eigel, Oliver G. Ernst, Björn Sprungk, Lorenzo Tamellini |
|---|---|
| Rok vydání: | 2022 |
| Předmět: |
parametric PDEs
65D15 65D05 Numerical Analysis convergence sparse grids Applied Mathematics Numerical Analysis (math.NA) 35R60 65D05 65D15 65N12 65C30 60H25 affine diffusion coefficient stochastic collocation Mathematics::Numerical Analysis residual error estimator Computational Mathematics Random PDEs a posteriori adaptivity 60H25 FOS: Mathematics 65C30 Mathematics - Numerical Analysis |
| Zdroj: | SIAM Journal on Numerical Analysis. 60:659-687 |
| ISSN: | 1095-7170 0036-1429 |
| Popis: | 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. Comment: 24 pages, 1 figure |
| Databáze: | OpenAIRE |
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