Multi-level Monte Carlo Finite Difference and Finite Volume Methods for Stochastic Linear Hyperbolic Systems

DOI10.1007/978-3-642-41095-6_34zbMath1302.65032OpenAlexW2276701498MaRDI QIDQ2926244

Siddhartha Mishra, Christoph Schwab, J. Šukys

Publication date: 31 October 2014

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/20.500.11850/154957

zbMATH Keywords

error boundnumerical experimentmulti-level Monte Carlo finite difference and finite volume algorithmsrandom weak solutionstochastic linear hyperbolic systems of conservation laws

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) 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) Complexity and performance of numerical algorithms (65Y20) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08) Initial value problems for first-order hyperbolic equations (35L03)

Related Items (6)

Stochastic Galerkin method for cloud simulation ⋮ A MultiOrder Discontinuous Galerkin Monte Carlo Method for Hyperbolic Problems with Stochastic Parameters ⋮ Entropies and Symmetrization of Hyperbolic Stochastic Galerkin Formulations ⋮ Uncertainty Quantification for Hyperbolic Conservation Laws with Flux Coefficients Given by Spatiotemporal Random Fields ⋮ Multi-level Monte Carlo finite volume methods for uncertainty quantification of acoustic wave propagation in random heterogeneous layered medium ⋮ Analysis of the Zero Relaxation Limit of Hyperbolic Balance Laws with Random Initial Data

Cites Work

• Unnamed Item
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• Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients
• Multi-level Monte Carlo finite volume methods for nonlinear systems of conservation laws in multi-dimensions
• Multi-level Monte Carlo finite element method for elliptic PDEs with stochastic coefficients
• Uniformly high order accurate essentially non-oscillatory schemes. III
• Strong Stability-Preserving High-Order Time Discretization Methods
• Sparse tensor multi-level Monte Carlo finite volume methods for hyperbolic conservation laws with random initial data
• Multilevel Monte Carlo Path Simulation
• Finite Volume Methods for Hyperbolic Problems
• Multilevel Monte Carlo Finite Volume Methods for Shallow Water Equations with Uncertain Topography in Multi-dimensions

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