A stochastic collocation method for the second-order wave equation with a discontinuous random speed

DOI10.1007/s00211-012-0493-5zbMath1268.65008OpenAlexW1967117214MaRDI QIDQ1939649

Raúl Tempone, Mohammad Motamed, Fabio Nobile

Publication date: 5 March 2013

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://infoscience.epfl.ch/record/180196/files/2013_Motamed_Nobile_Tempone_NumMath_StochWaves.pdf

zbMATH Keywords

convergencenumerical resultswave equationerror estimatesstochastic collocationfull and sparse tensor productsgenerogeneous media

Mathematics Subject Classification ID

Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

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Cites Work

• Unnamed Item
• Unnamed Item
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• Unnamed Item
• Unnamed Item
• Unnamed Item
• Uncertainty propagation using Wiener-Haar expansions
• Multi-resolution analysis of Wiener-type uncertainty propagation schemes
• Numerical homogenization of the acoustic wave equations with a continuum of scales
• Analyticity of solutions for a generalized Euler equation
• Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation
• Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations
• Sparse second moment analysis for elliptic problems in stochastic domains
• Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems
• Stochastic modeling of random roughness in shock scattering problems: theory and simulations
• EQSM: an efficient high-quality surface grid generation method based on remeshing
• Uncertainty quantification for systems of conservation laws
• Partial differential equations. 4th ed
• Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos
• Roe solver with entropy corrector for uncertain hyperbolic systems
• High dimensional polynomial interpolation on sparse grids
• A fictitious domain approach to the numerical solution of PDEs in stochastic domains
• Predicting shock dynamics in the presence of uncertainties
• On interpolation. I. Quadrature- and mean-convergence in the Lagrange- interpolation
• Implementation of optimal Galerkin and Collocation approximations of PDEs with Random Coefficients
• Strong and Weak Error Estimates for Elliptic Partial Differential Equations with Random Coefficients
• Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients
• Numerical Methods for Differential Equations in Random Domains
• A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
• An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
• Analysis and implementation issues for the numerical approximation of parabolic equations with random coefficients
• Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations
• Difference Approximations for the Second Order Wave Equation
• The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
• Initial-Boundary Value Problems and the Navier-Stokes Equations
• Convergence Analysis for Stochastic Collocation Methods to Scalar Hyperbolic Equations with a Random Wave Speed
• Spectral Methods
• High-Order Collocation Methods for Differential Equations with Random Inputs
• The Homogeneous Chaos
• A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
• Microlocal analysis of a seismic linearized inverse problem.

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