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Stochastic Collocation for Elliptic PDEs with Random Data: The Lognormal Case
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Stochastic Collocation for Elliptic PDEs with Random Data: The Lognormal Case (2014)Stochastic Collocation for Elliptic PDEs …Strong and Weak Error Estimates for Elliptic Partial Differential Equations with Random Coefficients (2012)Strong and Weak Error Estimat…ON THE OPTIMAL POLYNOMIAL APPROXIMATION OF STOCHASTIC PDES BY GALERKIN AND COLLOCATION METHODS (2012)ON THE OPTIMAL POLYNOMIAL APP…A Priori Error Analysis of Stochastic Galerkin Mixed Approximations of Elliptic PDEs with Random Data (2012)A Priori Error Analysis of St…Sparse tensor discretizations of high-dimensional parametric and stochastic PDEs (2011)Sparse tensor discretizations…On the convergence of generalized polynomial chaos expansions (2011)On the convergence of general…A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2010)A Stochastic Collocation Meth…Stochastic collocation and mixed finite elements for flow in porous media (2008)Stochastic collocation and mi…An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2008)An Anisotropic Sparse Grid St…A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2008)A Sparse Grid Stochastic Coll…A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2007)A Stochastic Collocation Meth…High-Order Collocation Methods for Differential Equations with Random Inputs (2005)High-Order Collocation Method…Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations (2004)Galerkin Finite Element Appro…Stochastic Finite Elements: A Spectral Approach (1991)Stochastic Finite Elements: A…Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems (2003)An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations (2009)A non-adapted sparse approximation of PDEs with stochastic inputs (2011)The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (2002)An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis (2009)Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization (2018)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)Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics (2008)An Introduction to Computational Stochastic PDEs (2014)Stochastic Integration and Differential Equations (2005)Adaptive stochastic Galerkin FEM (2013)Risk-Averse PDE-Constrained Optimization Using the Conditional Value-At-Risk (2016)Rectified deep neural networks overcome the curse of dimensionality for nonsmooth value functions in zero-sum games of nonlinear stiff systems (2020)Large Sample Properties of Simulations Using Latin Hypercube Sampling (1987)Adaptive sparse polynomial chaos expansion based on least angle regression (2010)Global sensitivity analysis using polynomial chaos expansions (2007)AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation (2011)Recent Developments in Spectral Stochastic Methods for the Numerical Solution of Stochastic Partial Differential Equations (2009)An adaptive high-dimensional stochastic model representation technique for the solution of stochastic partial differential equations (2010)Multi-level Monte Carlo Finite Element method for elliptic PDEs with stochastic coefficients (2011)Uncertainty Quantification and Weak Approximation of an Elliptic Inverse Problem (2011)A Multilevel Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2015)Analytic regularity and collocation approximation for elliptic PDEs with random domain deformations (2016)DAKOTA : a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis. Version 5.0, user's manual. (2010)Adaptive Smolyak Pseudospectral Approximations (2013)Sparse Polynomial Chaos Expansions: Literature Survey and Benchmark (2021)
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References

  • 1991Stochastic Finite Elements: A Spectral Approach5,753 cited
  • 2005High-Order Collocation Methods for Differential Equations with Random Inputs1,522 cited
  • 2007A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data1,396 cited
  • 2008A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data942 cited
  • 2004Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations869 cited
  • 2008An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data494 cited
  • 2011On the convergence of generalized polynomial chaos expansions414 cited
  • 2010A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data400 cited
  • 2011Sparse tensor discretizations of high-dimensional parametric and stochastic PDEs260 cited
  • 2012Strong and Weak Error Estimates for Elliptic Partial Differential Equations with Random Coefficients154 cited
  • 2012ON THE OPTIMAL POLYNOMIAL APPROXIMATION OF STOCHASTIC PDES BY GALERKIN AND COLLOCATION METHODS136 cited
  • 2008Stochastic collocation and mixed finite elements for flow in porous media59 cited
  • 2012A Priori Error Analysis of Stochastic Galerkin Mixed Approximations of Elliptic PDEs with Random Data22 cited

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