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It has recently been demonstrated that locality of spatial supports in the parametrization of coefficients in elliptic PDEs can lead to improved convergence rates of sparse polynomial expansions of the corresponding parameter-dependent solutions.
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J. Beck, F. Nobile, L. Tamellini, and R. Tempone, Convergence of quasi-optimal stochastic Galerkin methods for a class of PDEs with random coefficients
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M. Bachmayr, A. Cohen, R. DeVore, G. Migliorati, Sparse polynomial approximation of parametric elliptic PDEs. Part II: lognormal coefficients, ESAIM: M2AN 51
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