Parametric uncertainty analysis of pulse wave propagation in a model of a human arterial network
Journal of Computational Physics
The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications
Journal of Computational Physics
Efficient stochastic Galerkin methods for random diffusion equations
Journal of Computational Physics
A stochastic multiscale framework for modeling flow through random heterogeneous porous media
Journal of Computational Physics
Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems
Journal of Computational Physics
Journal of Computational Physics
A least-squares approximation of partial differential equations with high-dimensional random inputs
Journal of Computational Physics
Padé-Legendre approximants for uncertainty analysis with discontinuous response surfaces
Journal of Computational Physics
Journal of Computational Physics
Multi-element probabilistic collocation method in high dimensions
Journal of Computational Physics
Journal of Computational Physics
A finite element method for elliptic problems with stochastic input data
Applied Numerical Mathematics
Numerical approach for quantification of epistemic uncertainty
Journal of Computational Physics
Journal of Computational Physics
Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems
Journal of Computational Physics
Journal of Computational Physics
Probabilistic models for stochastic elliptic partial differential equations
Journal of Computational Physics
Adaptive sparse polynomial chaos expansion based on least angle regression
Journal of Computational Physics
A non-adapted sparse approximation of PDEs with stochastic inputs
Journal of Computational Physics
Sparse Tensor Discretization of Elliptic sPDEs
SIAM Journal on Scientific Computing
Iterative Solvers for the Stochastic Finite Element Method
SIAM Journal on Scientific Computing
A Kronecker Product Preconditioner for Stochastic Galerkin Finite Element Discretizations
SIAM Journal on Scientific Computing
Parameter and State Model Reduction for Large-Scale Statistical Inverse Problems
SIAM Journal on Scientific Computing
Quasi-Monte Carlo methods for elliptic PDEs with random coefficients and applications
Journal of Computational Physics
Characterization of discontinuities in high-dimensional stochastic problems on adaptive sparse grids
Journal of Computational Physics
A stochastic mixed finite element heterogeneous multiscale method for flow in porous media
Journal of Computational Physics
Kernel principal component analysis for stochastic input model generation
Journal of Computational Physics
Stochastic Galerkin methods for elliptic interface problems with random input
Journal of Computational and Applied Mathematics
Spectral Methods for Parameterized Matrix Equations
SIAM Journal on Matrix Analysis and Applications
Preconditioning Stochastic Galerkin Saddle Point Systems
SIAM Journal on Matrix Analysis and Applications
A Stochastic Mortar Mixed Finite Element Method for Flow in Porous Media with Multiple Rock Types
SIAM Journal on Scientific Computing
Error Estimates of Stochastic Optimal Neumann Boundary Control Problems
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Multiscale Stochastic Preconditioners in Non-intrusive Spectral Projection
Journal of Scientific Computing
Galerkin Methods for Stochastic Hyperbolic Problems Using Bi-Orthogonal Polynomials
Journal of Scientific Computing
Euro-Par'11 Proceedings of the 2011 international conference on Parallel Processing
Multi-output local Gaussian process regression: Applications to uncertainty quantification
Journal of Computational Physics
A method for solving stochastic equations by reduced order models and local approximations
Journal of Computational Physics
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
A Posteriori Error Analysis of Parameterized Linear Systems Using Spectral Methods
SIAM Journal on Matrix Analysis and Applications
Strong and Weak Error Estimates for Elliptic Partial Differential Equations with Random Coefficients
SIAM Journal on Numerical Analysis
A Sparse Composite Collocation Finite Element Method for Elliptic SPDEs.
SIAM Journal on Numerical Analysis
Uncertainty Quantification and Weak Approximation of an Elliptic Inverse Problem
SIAM Journal on Numerical Analysis
Wave scattering by randomly shaped objects
Applied Numerical Mathematics
Error analysis of generalized polynomial chaos for nonlinear random ordinary differential equations
Applied Numerical Mathematics
Journal of Computational Physics
An upscaling method using coefficient splitting and its applications to elliptic PDEs
Computers & Mathematics with Applications
Simplex stochastic collocation with ENO-type stencil selection for robust uncertainty quantification
Journal of Computational Physics
A flexible numerical approach for quantification of epistemic uncertainty
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Extended stochastic FEM for diffusion problems with uncertain material interfaces
Computational Mechanics
Combination technique based k-th moment analysis of elliptic problems with random diffusion
Journal of Computational Physics
Subcell resolution in simplex stochastic collocation for spatial discontinuities
Journal of Computational Physics
Uncertainty quantification for algebraic systems of equations
Computers and Structures
Uncertainty quantification for integrated circuits: stochastic spectral methods
Proceedings of the International Conference on Computer-Aided Design
Journal of Computational Physics
Computers & Mathematics with Applications
High-order methods as an alternative to using sparse tensor products for stochastic Galerkin FEM
Computers & Mathematics with Applications
Comparison Between Reduced Basis and Stochastic Collocation Methods for Elliptic Problems
Journal of Scientific Computing
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In this paper we propose and analyze a stochastic collocation method to solve elliptic partial differential equations with random coefficients and forcing terms (input data of the model). The input data are assumed to depend on a finite number of random variables. The method consists in a Galerkin approximation in space and a collocation in the zeros of suitable tensor product orthogonal polynomials (Gauss points) in the probability space and naturally leads to the solution of uncoupled deterministic problems as in the Monte Carlo approach. It can be seen as a generalization of the stochastic Galerkin method proposed in [I. Babusˇka, R. Tempone, and G. E. Zouraris, SIAM J. Numer. Anal., 42 (2004), pp. 800-825] and allows one to treat easily a wider range of situations, such as input data that depend nonlinearly on the random variables, diffusivity coefficients with unbounded second moments, and random variables that are correlated or even unbounded. We provide a rigorous convergence analysis and demonstrate exponential convergence of the “probability error” with respect to the number of Gauss points in each direction in the probability space, under some regularity assumptions on the random input data. Numerical examples show the effectiveness of the method.