Stochastic collocation with kernel density estimation

DOI10.1016/j.cma.2012.06.020zbMath1354.65258OpenAlexW1997572111MaRDI QIDQ503927

Howard C. Elman, Christopher W. Miller

Publication date: 24 January 2017

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2012.06.020

zbMATH Keywords

stochastic partial differential equationkernel density estimationadaptivestochastic collocation

Mathematics Subject Classification ID

Density estimation (62G07) Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs (65N75) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35)

Related Items

From Data to Uncertainty: An Efficient Integrated Data-Driven Sparse Grid Approach to Propagate Uncertainty

Uses Software

• Spinterp
• BRENT

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients
• Probabilistic models for stochastic elliptic partial differential equations
• Multi-level Monte Carlo finite element method for elliptic PDEs with stochastic coefficients
• Solving elliptic problems with non-Gaussian spatially-dependent random coefficients
• Multi-element probabilistic collocation method in high dimensions
• The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications
• An adaptive high-dimensional stochastic model representation technique for the solution of stochastic partial differential equations
• An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations
• An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
• ASSESSMENT OF COLLOCATION AND GALERKIN APPROACHES TO LINEAR DIFFUSION EQUATIONS WITH RANDOM DATA
• Algorithm 847
• A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
• An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
• Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations
• High-Order Collocation Methods for Differential Equations with Random Inputs
• The Monte Carlo Method
• A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data