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Multi-level Monte Carlo Finite Volume Methods for Uncertainty Quantification in Nonlinear Systems of Balance Laws
14 references·4 citing·32 second hopsampled
Multi-level Monte Carlo Finite Volume Methods for Uncertainty Quantification in Nonlinear Systems of Balance Laws (2013)Multi-level Monte Carlo Finite Volume Met…Sparse tensor multi-level Monte Carlo finite volume methods for hyperbolic conservation laws with random initial data (2012)Sparse tensor multi-level Mon…Multilevel Monte Carlo Finite Volume Methods for Shallow Water Equations with Uncertain Topography in Multi-dimensions (2012)Multilevel Monte Carlo Finite…Multi-level Monte Carlo finite volume methods for nonlinear systems of conservation laws in multi-dimensions (2012)Multi-level Monte Carlo finit…Multi-level Monte Carlo Finite Element method for elliptic PDEs with stochastic coefficients (2011)Multi-level Monte Carlo Finit…Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems (2010)Intrusive Galerkin methods wi…An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations (2009)An adaptive hierarchical spar…Uncertainty quantification for systems of conservation laws (2008)Uncertainty quantification fo…Multilevel Monte Carlo Path Simulation (2008)Multilevel Monte Carlo Path S…An adaptive Stochastic Finite Elements approach based on Newton–Cotes quadrature in simplex elements (2008)An adaptive Stochastic Finite…Improved Multilevel Monte Carlo Convergence using the Milstein Scheme (2007)Improved Multilevel Monte Car…Sparse finite element methods for operator equations with stochastic data (2006)Sparse finite element methods…Long-term behavior of polynomial chaos in stochastic flow simulations (2006)Long-term behavior of polynom…High-Order Collocation Methods for Differential Equations with Random Inputs (2005)High-Order Collocation Method…Uncertainty analysis for the steady-state flows in a dual throat nozzle (2004)Uncertainty analysis for the …Multilevel Monte Carlo finite volume methods for random conservation laws with discontinuous flux (2021)Multilevel Monte Carlo finite…Stochastic Galerkin method for cloud simulation (2019)Stochastic Galerkin method fo…Multilevel Monte Carlo front-tracking for random scalar conservation laws (2015)Multilevel Monte Carlo front-…Adaptive Load Balancing for Massively Parallel Multi-Level Monte Carlo Solvers (2014)Adaptive Load Balancing for M…Stochastic Finite Elements: A Spectral Approach (1991)The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (2002)A stochastic Galerkin method for the Euler equations with Roe variable transformation (2013)Adaptive stochastic Galerkin FEM (2013)A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2007)A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2008)Finite Element Error Analysis of Elliptic PDEs with Random Coefficients and Its Application to Multilevel Monte Carlo Methods (2013)Further analysis of multilevel Monte Carlo methods for elliptic PDEs with random coefficients (2013)Stochastic finite element methods for partial differential equations with random input data (2014)Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations (2004)Stochastic Differential Equations: An Introduction with Applications. (1987)A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2010)A non-adapted sparse approximation of PDEs with stochastic inputs (2011)Monte Carlo Methods in Financial Engineering (2003)An Euler-type method for the strong approximation of the Cox–Ingersoll–Ross process (2011)Monte Carlo and Quasi-Monte Carlo Methods (2013)Unbiased Estimation with Square Root Convergence for SDE Models (2015)Numerical solution of stochastic differential equations (2016)Proceedings of the 2004 Winter Simulation Conference, 2004. 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References

  • 2005High-Order Collocation Methods for Differential Equations with Random Inputs1,522 cited
  • 2008Multilevel Monte Carlo Path Simulation1,436 cited
  • 2009An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations447 cited
  • 2011Multi-level Monte Carlo Finite Element method for elliptic PDEs with stochastic coefficients296 cited
  • 2007Improved Multilevel Monte Carlo Convergence using the Milstein Scheme205 cited
  • 2008Uncertainty quantification for systems of conservation laws177 cited
  • 2006Long-term behavior of polynomial chaos in stochastic flow simulations173 cited
  • 2012Sparse tensor multi-level Monte Carlo finite volume methods for hyperbolic conservation laws with random initial data142 cited
  • 2010Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems127 cited
  • 2012Multi-level Monte Carlo finite volume methods for nonlinear systems of conservation laws in multi-dimensions113 cited
  • 2004Uncertainty analysis for the steady-state flows in a dual throat nozzle74 cited
  • 2006Sparse finite element methods for operator equations with stochastic data70 cited
  • 2008An adaptive Stochastic Finite Elements approach based on Newton–Cotes quadrature in simplex elements64 cited
  • 2012Multilevel Monte Carlo Finite Volume Methods for Shallow Water Equations with Uncertain Topography in Multi-dimensions

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48 cited

Cited by

  • 2021Multilevel Monte Carlo finite volume methods for random conservation laws with discontinuous flux13 cited
  • 2019Stochastic Galerkin method for cloud simulation13 cited
  • 2015Multilevel Monte Carlo front-tracking for random scalar conservation laws12 cited
  • 2014Adaptive Load Balancing for Massively Parallel Multi-Level Monte Carlo Solvers10 cited