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A semi-intrusive deterministic approach to uncertainty quantification in non-linear fluid flow problems
16 references·10 citing·28 second hop
A semi-intrusive deterministic approach to uncertainty quantification in non-linear fluid flow problems (2012)A semi-intrusive deterministic approach t…Time-dependent generalized polynomial chaos (2010)Time-dependent generalized po…Fast Numerical Methods for Stochastic Computations: A Review (2009)Fast Numerical Methods for St…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…Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics (2008)Uncertainty Quantification an…The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications (2008)The multi-element probabilist…Wiener Chaos expansions and numerical solutions of randomly forced equations of fluid mechanics (2006)Wiener Chaos expansions and n…Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures (2006)Multi-Element Generalized Pol…Long-term behavior of polynomial chaos in stochastic flow simulations (2006)Long-term behavior of polynom…An adaptive multi-element generalized polynomial chaos method for stochastic differential equations (2005)An adaptive multi-element gen…Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations (2004)Galerkin Finite Element Appro…Uncertainty quantification in reacting-flow simulations through non-intrusive spectral projection (2003)Uncertainty quantification in…The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (2002)The Wiener--Askey Polynomial …A Stochastic Projection Method for Fluid Flow (2002)A Stochastic Projection Metho…A Stochastic Projection Method for Fluid Flow (2001)A Stochastic Projection Metho…Stochastic Finite Elements: A Spectral Approach (1991)Stochastic Finite Elements: A…Sensitivity equation method for the Navier‐Stokes equations applied to uncertainty propagation (2020)Sensitivity equation method f…Uncertainty quantification methodology for hyperbolic systems with application to blood flow in arteries (2019)Uncertainty quantification me…A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty (2017)A stochastic Galerkin method …Computational uncertainty quantification for a clarifier-thickener model with several random perturbations: A hybrid stochastic Galerkin approach (2016)Computational uncertainty qua…A Stochastic Galerkin Method for Hamilton--Jacobi Equations with Uncertainty (2015)A Stochastic Galerkin Method …A Novel Weakly-Intrusive Non-linear Multiresolution Framework for Uncertainty Quantification in Hyperbolic Partial Differential Equations (2015)A Novel Weakly-Intrusive Non-…Variance reduction through robust design of boundary conditions for stochastic hyperbolic systems of equations (2014)Variance reduction through ro…Subcell resolution in simplex stochastic collocation for spatial discontinuities (2013)Subcell resolution in simplex…Dynamic Adaptive Sampling Based on Kriging Surrogate Models for Efficient Uncertainty Quantification (2013)Dynamic Adaptive Sampling Bas…A one-time truncate and encode multiresolution stochastic framework (2013)A one-time truncate and encod…Ingredients for a general purpose stochastic finite elements implementation (1999)Multi-resolution analysis of Wiener-type uncertainty propagation schemes (2004)Combustion kinetic model uncertainty quantification, propagation and minimization (2014)Modeling uncertainty in flow simulations via generalized polynomial chaos (2003)A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2010)Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion (2012)Random vibration and statistical linearization (1990)Verification and Validation in Computational Science and Engineering (1998)Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations (2004)An Introduction to Computational Stochastic PDEs (2014)Stochastic Differential Equations: An Introduction with Applications. 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References

  • 1991Stochastic Finite Elements: A Spectral Approach5,753 cited
  • 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 cited
  • 2004Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations869 cited
  • 2008Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics769 cited
  • 2009Fast Numerical Methods for Stochastic Computations: A Review608 cited
  • 2005An adaptive multi-element generalized polynomial chaos method for stochastic differential equations578 cited
  • 2002A Stochastic Projection Method for Fluid Flow503 cited
  • 2006Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures498 cited
  • 2009An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations447 cited
  • 2001A Stochastic Projection Method for Fluid Flow338 cited
  • 2003Uncertainty quantification in reacting-flow simulations through non-intrusive spectral projection333 cited
  • 2008The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications214 cited
  • 2006Wiener Chaos expansions and numerical solutions of randomly forced equations of fluid mechanics194 cited
  • 2008Uncertainty quantification for systems of conservation laws

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177 cited
  • 2010Time-dependent generalized polynomial chaos173 cited
  • 2006Long-term behavior of polynomial chaos in stochastic flow simulations173 cited
  • Cited by

    • 2017A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty28 cited
    • 2015A Stochastic Galerkin Method for Hamilton--Jacobi Equations with Uncertainty24 cited
    • 2020Sensitivity equation method for the Navier‐Stokes equations applied to uncertainty propagation24 cited
    • 2013Dynamic Adaptive Sampling Based on Kriging Surrogate Models for Efficient Uncertainty Quantification23 cited
    • 2016Computational uncertainty quantification for a clarifier-thickener model with several random perturbations: A hybrid stochastic Galerkin approach17 cited
    • 2013Subcell resolution in simplex stochastic collocation for spatial discontinuities16 cited
    • 2014Variance reduction through robust design of boundary conditions for stochastic hyperbolic systems of equations15 cited
    • 2013A one-time truncate and encode multiresolution stochastic framework14 cited
    • 2015A Novel Weakly-Intrusive Non-linear Multiresolution Framework for Uncertainty Quantification in Hyperbolic Partial Differential Equations12 cited
    • 2019Uncertainty quantification methodology for hyperbolic systems with application to blood flow in arteries12 cited