Convergence of an adaptive collocation method for the parametric stationary 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 a hierarchical error estimator is transferred to the collocation setting. Extensions to other variants of adaptive collocation methods (including the now classical approach proposed in [T. Gerstner and M. Griebel, Computing, 71 (2003), pp. 65-87]) are explored.

On the convergence of adaptive stochastic collocation for elliptic partial differential equations with affine diffusion

L Tamellini
2022

Abstract

Convergence of an adaptive collocation method for the parametric stationary 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 a hierarchical error estimator is transferred to the collocation setting. Extensions to other variants of adaptive collocation methods (including the now classical approach proposed in [T. Gerstner and M. Griebel, Computing, 71 (2003), pp. 65-87]) are explored.
2022
Istituto di Matematica Applicata e Tecnologie Informatiche - IMATI -
adaptive algorithms
high-dimensional approximation
high-dimensional interpolation
parametric PDEs
random PDEs
sparse grids
stochastic collocation
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.14243/465041
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