Citation map · Study

SZodixStudyAcademic Library

Shelves Open access

Study · an open academic library·Metadata from OpenAlex (CC0)·Shelves·OpenAlex metadata, de-duplicated

The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications

15 references·16 citing·20 second hop

FromToDepth

this work references cited by second hop

References

1991Stochastic Finite Elements: A Spectral Approach5,753 cited
2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 cited
2003Stochastic Differential Equations2,978 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
2005An adaptive multi-element generalized polynomial chaos method for stochastic differential equations578 cited
2004Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations556 cited
2006Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures498 cited
2008An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data494 cited
2001Solution of stochastic partial differential equations using Galerkin finite element techniques414 cited
2007Sparse grid collocation schemes for stochastic natural convection problems401 cited
2004Finite elements for elliptic problems with stochastic coefficients

Only edges whose both ends are imported exist here. Widen the year window, or show the whole map. Back to the work

364 cited

2004Multi-resolution analysis of Wiener-type uncertainty propagation schemes335 cited

Cited by

2009Multi-element probabilistic collocation method in high dimensions203 cited
2010Adaptive-sparse polynomial chaos expansion for reliability analysis and design of complex engineering systems183 cited
2010Time-dependent generalized polynomial chaos173 cited
2010Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems127 cited
2013Reweighted minimization method for stochastic elliptic differential equations108 cited
2010Numerical approach for quantification of epistemic uncertainty98 cited
2009A domain adaptive stochastic collocation approach for analysis of MEMS under uncertainties88 cited
2012Stochastic Collocation Methods on Unstructured Grids in High Dimensions via Interpolation73 cited
2015An ME-PC Enhanced HDMR Method for Efficient Statistical Analysis of Multiconductor Transmission Line Networks71 cited
2014Computational Aspects of Stochastic Collocation with Multifidelity Models67 cited
2010Non-Intrusive Polynomial Chaos Methods for Uncertainty Quantification in Fluid Dynamics66 cited
2012Simplex Stochastic Collocation with Random Sampling and Extrapolation for Nonhypercube Probability Spaces63 cited
2010A stochastic collocation method for large classes of mechanical problems with uncertain parameters61 cited
2009A gPC-based approach to uncertain transonic aerodynamics54 cited
2013Grid and basis adaptive polynomial chaos techniques for sensitivity and uncertainty analysis52 cited
2010Comput. Methods Appl. Mech. Engrg.51 cited