Finite elements for elliptic problems with stochastic coefficients

By P. Frauenfelder, Christoph Schwab, Radu Alexandru Todor. 2005

408 citations recorded by the source corpus.

Subfields: Environmental Engineering, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/cebf5316774003faae63be2ecc7150cbe8c6d29b

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In Environmental Engineering

In Statistical and Nonlinear Physics

In Statistics and Probability

Citations in the corpus

Long-Term Behavior of Polynomial Chaos in Stochastic Flow Simulations (2006, methodology): “We subsequently decompose the middle element [ 6,6] while keeping the tail elements unchanged since Pr(n 2 ( 1, 6] or [6,1)) = 1.”
Solving elliptic problems with non-Gaussian spatially-dependent random coefficients (2009, methodology): “For more discussions about the decay rate of ki we refer to [13].”
Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures (2006, methodology): “To solve differential equations with stochastic inputs following the procedure established by Ghanem and Spanos, the random solution is expanded spectrally by PC, and a Galerkin projection scheme is subsequently used to transform the original stochastic problem into a deterministic one with a larger”
A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2008, neutral): “Observe that, in the latter case, as √ λn‖bn‖L∞(D) → 0 for a regular enough covariance function (see [16]) the analyticity region increases as n increases.”
Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients (2007, background): “Tensor-product discretization or tensor-product collocation grids in the parametric variable result, however, in superalgebraic complexity rates (see, e.g. Babuška et al., 2004; Frauenfelder et al., 2005; Matthies & Keese, 2005).”
Numerical methods for the discretization of random fields by means of the Karhunen–Loève expansion (2014, methodology): “For the computation of the matrix eigenvalue problem in the FEM, a generalized fast multi-pole Krylov eigen-solver is used in [11, 12].”
High-Order Collocation Methods for Differential Equations with Random Inputs (2005, methodology): “They are employed in [2, 15], and the number of basis functions in Z N is dim(Z p N ) = (p + 1) N .”
Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems (2008, methodology): “These developments include adaptive polynomial degree and sparse truncations of the PC basis [34, 75], and other methods of stochastic model reduction [76].”
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2007, background): “4) (see also [32, 4, 27, 62] and the references therein).”
An extended stochastic finite element method for solving stochastic partial differential equations on random domains (2008, neutral): “[1–3,33]).”