STOCHASTIC GALERKIN DISCRETIZATION OF THE LOG-NORMAL ISOTROPIC DIFFUSION PROBLEM

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Sparse tensor discretizations of high-dimensional parametric and stochastic PDEs* (2011, methodology): “Given a space VN , the Galerkin projection uN of u onto VN can be computed iteratively, for example by a conjugate gradient iteration; see Gittelson (2011b). The inverse of the deterministic operator Ā can be used as a preconditioner.”
Efficient low-rank approximation of the stochastic Galerkin matrix in tensor formats (2014, background): “Nevertheless, in [22] or [10] it is shown that under additional assumptions to the right-hand side f and special choices of V the weak formulation is well-posed.”
Approximation of high-dimensional parametric PDEs * (2015, background): “In a similar infinite dimensional framework, and not covered in our paper, let us mention the following related works: (i) similar holomorphy and approximation results are established in [47, 48, 58] for specific type of PDEs and control problems, (ii) approximation of integrals by quadratures is di”
N-term Wiener chaos approximation rates for elliptic PDEs with lognormal Gaussian random inputs (2014, background): “✷ Next, we review solvability of elliptic problems with log-normal coefficients as discussed in [13] and [22] to the extent that we require later.”
Sparse polynomial approximation of parametric elliptic PDEs. Part II: lognormal coefficients (2015, unknown): “This particular issue has been dealt with in papers such as [5, 13, 16, 12].”