Stochastic Collocation Methods for Nonlinear Parabolic Equations with Random Coefficients

DOI10.1137/130930108zbMath1343.65005OpenAlexW2342750049MaRDI QIDQ5741187

David A. Barajas-Solano, Daniel M. Tartakovsky

Publication date: 22 July 2016

Published in: SIAM/ASA Journal on Uncertainty Quantification (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/76dc3212139e8819f8079d7b54b8e4bf4084f54a

zbMATH Keywords

Monte Carlo simulationsrandom coefficientscomputational efficiencynonlinear diffusionuncertainty quantificationRichards equationstochastic collocationnonlinear parabolic and elliptic problems

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Nonlinear parabolic equations (35K55) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Nonlinear elliptic equations (35J60) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Complexity and performance of numerical algorithms (65Y20)

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Uses Software

• SUNDIALS
• RADAU
• PATSYM
• HRMSYM

Cites Work

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• SUNDIALS
• Characterization of discontinuities in high-dimensional stochastic problems on adaptive sparse grids
• Uncertainty propagation using Wiener-Haar expansions
• Multi-resolution analysis of Wiener-type uncertainty propagation schemes
• A domain adaptive stochastic collocation approach for analysis of MEMS under uncertainties
• Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation
• The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications
• Strong solutions to the Richards equation in the unsaturated zone
• Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems
• Discontinuity detection in multivariate space for stochastic simulations
• An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations
• Nonexistence of extended Gauss-Laguerre and Gauss-Hermite quadrature rules with positive weights
• Numerical integration using sparse grids
• Explicit cost bounds of algorithms for multivariate tensor product problems
• Finite elements for elliptic problems with stochastic coefficients
• Stochastic analysis of effective rate constant for heterogeneous reactions
• Fully symmetric interpolatory rules for multiple integrals over infinite regions with Gaussian weight
• Simple cubature formulas with high polynomial exactness
• Stiff differential equations solved by Radau methods
• Sparse grid collocation schemes for stochastic natural convection problems
• High dimensional integration of smooth functions over cubes
• Strong and Weak Error Estimates for Elliptic Partial Differential Equations with Random Coefficients
• Cubature formulas for symmetric measures in higher dimensions with few points
• Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures
• Numerical Cubature Using Error-Correcting Codes
• Eulerian Moment Equations for 2-D Stochastic Immiscible Flow
• Stochastic averaging of nonlinear flows in heterogeneous porous media
• Higher-Dimensional Integration with Gaussian Weight for Applications in Probabilistic Design
• Asymmetric Cubature Formulae with Few Points in High Dimension for Symmetric Measures