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Robust goal-oriented error estimation based on the constitutive relation error for stochastic problems
9 references·0 citing·36 second hop
Robust goal-oriented error estimation based on the constitutive relation error for stochastic problems (2012)Robust goal-oriented error estimation bas…The stochastic finite element method: Past, present and future (2008)The stochastic finite element…A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2007)A Stochastic Collocation Meth…Verification of stochastic models in uncertain environments using the constitutive relation error method (2006)Verification of stochastic mo…Theory and methodology for estimation and control of errors due to modeling, approximation, and uncertainty (2004)Theory and methodology for es…Eléments finis stochastiques en élasticité linéaire (2004)Eléments finis stochastiques …Solution of stochastic partial differential equations using Galerkin finite element techniques (2001)Solution of stochastic partia…Finite elements for stochastic media problems (1999)Finite elements for stochasti…A state-of-the-art report on computational stochastic mechanics (1997)A state-of-the-art report on …Stochastic Finite Elements: A Spectral Approach (1991)Stochastic Finite Elements: A…A multigrid solver for two-dimensional stochastic diffusion equations (2003)Stochastic Differential Equations (2003)QUANTIFYING UNCERTAINTY: MODERN COMPUTATIONAL REPRESENTATION OF PROBABILITY AND APPLICATIONS (2007)Sampling-free linear Bayesian update of polynomial chaos representations (2012)Numerical solution of stochastic differential equations (2016)Ingredients for a general purpose stochastic finite elements implementation (1999)Error estimation in a stochastic finite element method in electrokinetics (2009)Error bounds for the reliability index in finite element reliability analysis (2011)Enhanced goal‐oriented error assessment and computational strategies in adaptive reduced basis solver for stochastic problems (2016)The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (2002)High-Order Collocation Methods for Differential Equations with Random Inputs (2005)A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2008)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)Structural Reliability Methods (1996)Stochastic Analysis (1997)Current Calculation in Electrokinetics Using a Spectral Stochastic Finite Element Method (2008)Updating the long-term creep strains in concrete containment vessels by using Markov chain Monte Carlo simulation and polynomial chaos expansions (2010)Response Surfaces based on Polynomial Chaos Expansions (2013)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)Estimation of small failure probabilities in high dimensions by subset simulation (2001)Numerical methods for the discretization of random fields by means of the Karhunen–Loève expansion (2014)Direct probability integral method for stochastic response analysis of static and dynamic structural systems (2019)Recent Trends in the Modeling and Quantification of Non-probabilistic Uncertainty (2019)Global sensitivity analysis using polynomial chaos expansions (2007)AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation (2011)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)Uncertainty Quantification with Stochastic Finite Elements (2004)Generalized stochastic perturbation technique in engineering computations (2009)Model order reduction accelerated Monte Carlo stochastic isogeometric method for the analysis of structures with high-dimensional and independent material uncertainties (2019)
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References

  • 1991Stochastic Finite Elements: A Spectral Approach5,753 cited
  • 2007A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data1,396 cited
  • 2008The stochastic finite element method: Past, present and future999 cited
  • 1997A state-of-the-art report on computational stochastic mechanics424 cited
  • 2001Solution of stochastic partial differential equations using Galerkin finite element techniques414 cited
  • 1999Finite elements for stochastic media problems89 cited
  • 2004Theory and methodology for estimation and control of errors due to modeling, approximation, and uncertainty70 cited
  • 2006Verification of stochastic models in uncertain environments using the constitutive relation error method27 cited
  • 2004Eléments finis stochastiques en élasticité linéaire21 cited

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