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• W2606283473 abstract "We give a convergence proof for the approximation by sparse collocation of Hilbert-space-valued functions depending on countably many Gaussian random variables. Such functions appear as solutions of elliptic PDEs with lognormal diffusion coefficients. We outline a general $L^2$-convergence theory based on previous work by Bachmayr et al. [ESAIM Math. Model. Numer. Anal., 51 (2017), pp. 341--363] and Chen [ESAIM Math. Model. Numer. Anal., in press, 2018, https://doi.org/10.1051/m2an/2018012] and establish an algebraic convergence rate for sufficiently smooth functions assuming a mild growth bound for the univariate hierarchical surpluses of the interpolation scheme applied to Hermite polynomials. We specifically verify for Gauss--Hermite nodes that this assumption holds and also show algebraic convergence with respect to the resulting number of sparse grid points for this case. Numerical experiments illustrate the dimension-independent convergence rate." @default.
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• W2606283473 date "2018-01-01" @default.
• W2606283473 modified "2023-10-17" @default.
• W2606283473 title "Convergence of Sparse Collocation for Functions of Countably Many Gaussian Random Variables (with Application to Elliptic PDEs)" @default.
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• W2606283473 doi "https://doi.org/10.1137/17m1123079" @default.
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