Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Journal of Computational and Applied Mathematics
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
Orthogonal series density estimation and the kernel eigenvalue problem
Neural Computation
Quarterly of Applied Mathematics
Robust Eigenvalue Computation for Smoothing Operators
SIAM Journal on Numerical Analysis
Karhunen-Loève approximation of random fields by generalized fast multipole methods
Journal of Computational Physics - Special issue: Uncertainty quantification in simulation science
Computational aspects of the stochastic finite element method
Computing and Visualization in Science
Statistical moments of the random linear transport equation
Journal of Computational Physics
Quasi-Monte Carlo methods for elliptic PDEs with random coefficients and applications
Journal of Computational Physics
A state-variable approach to the solution of Fredholm integral equations
IEEE Transactions on Information Theory
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We consider the numerical approximation of homogeneous Fredholm integral equations of second kind, with emphasis on computing truncated Karhunen-Loeve expansions. We employ the spectral element method with Gauss-Lobatto-Legendre (GLL) collocation points. Similar to the piecewise-constant finite elements, this approach is simple to implement and does not lead to generalized discrete eigenvalue problems. Numerical experiments confirm the expected convergence rates for some classical kernels and illustrate how this approach can improve the finite element solution of partial differential equations with random input data.