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Numerical Methods and Smolyak Quadrature for Nonlinear Stochastic Partial Differential Equations
16 references·16 citing·34 second hopsampled
Numerical Methods and Smolyak Quadrature for Nonlinear Stochastic Partial Differential Equations (2003)Numerical Methods and Smolyak Quadrature …Stochastic partial differential equations (2020)Stochastic partial differenti…Numerical solution of stochastic differential equations (2016)Numerical solution of stochas…Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations (2004)Galerkin methods for linear a…Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations (2004)Galerkin Finite Element Appro…The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (2002)The Wiener--Askey Polynomial …On solving elliptic stochastic partial differential equations (2002)On solving elliptic stochasti…Stochastic Modeling of Flow-Structure Interactions Using Generalized Polynomial Chaos (2001)Stochastic Modeling of Flow-S…Solution of stochastic partial differential equations using Galerkin finite element techniques (2001)Solution of stochastic partia…Reliability Assessment Using Stochastic Finite Element Analysis (2000)Reliability Assessment Using …Ingredients for a general purpose stochastic finite elements implementation (1999)Ingredients for a general pur…Uncertainties in probabilistic numerical analysis of structures and solids-Stochastic finite elements (1997)Uncertainties in probabilisti…Stochastic Analysis (1997)Stochastic AnalysisResponse Surfaces: Designs and Analyses (1997)Response Surfaces: Designs an…A state-of-the-art report on computational stochastic mechanics (1997)A state-of-the-art report on …The stochastic finite element method: basic perturbation technique and computer implementation (1993)The stochastic finite element…Stochastic Finite Elements: A Spectral Approach (1991)Stochastic Finite Elements: A…Sparse Pseudo Spectral Projection Methods with Directional Adaptation for Uncertainty Quantification (2015)Sparse Pseudo Spectral Projec…To be or not to be intrusive? The solution of parametric and stochastic equations - the "plain vanilla" Galerkin case. (2013)To be or not to be intrusive?…Polynomial Chaos expansion for subsurface flows with uncertain soil parameters (2013)Polynomial Chaos expansion fo…Competitive comparison of optimal designs of experiments for sampling-based sensitivity analysis (2013)Competitive comparison of opt…Acceleration of uncertainty updating in the description of transport processes in heterogeneous materials (2012)Acceleration of uncertainty u…On the Capabilities of the Polynomial Chaos Expansion Method within SFE Analysis—An Overview (2011)On the Capabilities of the Po…Multiscale Stochastic Preconditioners in Non-intrusive Spectral Projection (2011)Multiscale Stochastic Precond…Galerkin Methods for Stochastic Hyperbolic Problems Using Bi-Orthogonal Polynomials (2011)Galerkin Methods for Stochast…Convergence Analysis for Stochastic Collocation Methods to Scalar Hyperbolic Equations with a Random Wave Speed (2010)Convergence Analysis for Stoc…Sensitivity analysis and stochastic simulations of non‐equilibrium plasma flow (2009)Sensitivity analysis and stoc…Strain and stress computations in stochastic finite element methods (2007)Strain and stress computation…Stochastic simulation of riser-sections with uncertain measured pressure loads and/or uncertain material properties (2007)Stochastic simulation of rise…Quasi random numbers in stochastic finite element analysis (2007)Quasi random numbers in stoch…An analysis of polynomial chaos approximations for modeling single-fluid-phase flow in porous medium systems (2007)An analysis of polynomial cha…Verification of stochastic models in uncertain environments using the constitutive relation error method (2006)Verification of stochastic mo…Validation of structural dynamics models containing uncertainties (2005)Validation of structural dyna…The stochastic finite-element method (1980)Stochastic Differential Equations: An Introduction with Applications. (1987)Uncertainty propagation using Wiener–Haar expansions (2004)Sparse grid collocation schemes for stochastic natural convection problems (2007)A non-adapted sparse approximation of PDEs with stochastic inputs (2011)Statistics for experimenters. An introduction to design, data analysis, and model building. (1978)Empirical Model Building and Response Surfaces (1988)A new look at the response surface approach for reliability analysis (1993)Response Surface Methodology: Process and Product Optimization Using Designed Experiments (1996)Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems (2003)Response Surface Methodology: A Retrospective and Literature Survey (2004)Random vibration and statistical linearization (1990)Verification and Validation in Computational Science and Engineering (1998)Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics (2008)An Introduction to Computational Stochastic PDEs (2014)Global sensitivity analysis using polynomial chaos expansions (2007)AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation (2011)Martingale Methods in Financial Modelling (1997)Alternative models for stock price dynamics (2003)Multilevel Monte Carlo Path Simulation (2008)High-Order Collocation Methods for Differential Equations with Random Inputs (2005)Adaptive sparse polynomial chaos expansion based on least angle regression (2010)A generalized dimension‐reduction method for multidimensional integration in stochastic mechanics (2004)Probability density evolution method for dynamic response analysis of structures with uncertain parameters (2004)A GF-discrepancy for point selection in stochastic seismic response analysis of structures with uncertain parameters (2015)Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures (2006)An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2008)Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion (2012)Applications of Malliavin calculus to Monte Carlo methods in finance (1999)Stochastic Calculus with Respect to Gaussian Processes (2001)Stein’s method on Wiener chaos (2008)Comparison of response surface and neural network with other methods for structural reliability analysis (2003)A survey of non-probabilistic uncertainty treatment in finite element analysis (2004)Assessment of the efficiency of Kriging surrogate models for structural reliability analysis (2014)
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References

  • 1991Stochastic Finite Elements: A Spectral Approach5,753 cited
  • 2016Numerical solution of stochastic differential equations5,001 cited
  • 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 cited
  • 1997Response Surfaces: Designs and Analyses1,520 cited
  • 1997Stochastic Analysis1,035 cited
  • 2004Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations869 cited
  • 2004Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations556 cited
  • 2000Reliability Assessment Using Stochastic Finite Element Analysis524 cited
  • 1997A state-of-the-art report on computational stochastic mechanics424 cited
  • 2001Solution of stochastic partial differential equations using Galerkin finite element techniques414 cited
  • 1999Ingredients for a general purpose stochastic finite elements implementation401 cited
  • 1993The stochastic finite element method: basic perturbation technique and computer implementation400 cited
  • 1997Uncertainties in probabilistic numerical analysis of structures and solids-Stochastic finite elements354 cited
  • 2001Stochastic Modeling of Flow-Structure Interactions Using Generalized Polynomial Chaos273 cited
  • 2020

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Stochastic partial differential equations
216 cited
  • 2002On solving elliptic stochastic partial differential equations198 cited
  • Cited by

    • 2013Polynomial Chaos expansion for subsurface flows with uncertain soil parameters48 cited
    • 2005Validation of structural dynamics models containing uncertainties44 cited
    • 2010Convergence Analysis for Stochastic Collocation Methods to Scalar Hyperbolic Equations with a Random Wave Speed43 cited
    • 2013To be or not to be intrusive? The solution of parametric and stochastic equations - the "plain vanilla" Galerkin case.43 cited
    • 2007Quasi random numbers in stochastic finite element analysis43 cited
    • 2007Strain and stress computations in stochastic finite element methods37 cited
    • 2007Stochastic simulation of riser-sections with uncertain measured pressure loads and/or uncertain material properties35 cited
    • 2007An analysis of polynomial chaos approximations for modeling single-fluid-phase flow in porous medium systems34 cited
    • 2015Sparse Pseudo Spectral Projection Methods with Directional Adaptation for Uncertainty Quantification34 cited
    • 2011On the Capabilities of the Polynomial Chaos Expansion Method within SFE Analysis—An Overview32 cited
    • 2011Multiscale Stochastic Preconditioners in Non-intrusive Spectral Projection31 cited
    • 2006Verification of stochastic models in uncertain environments using the constitutive relation error method27 cited
    • 2012Acceleration of uncertainty updating in the description of transport processes in heterogeneous materials27 cited
    • 2013Competitive comparison of optimal designs of experiments for sampling-based sensitivity analysis27 cited
    • 2011Galerkin Methods for Stochastic Hyperbolic Problems Using Bi-Orthogonal Polynomials24 cited
    • 2009Sensitivity analysis and stochastic simulations of non‐equilibrium plasma flow22 cited