Numerical studies of three-dimensional stochastic Darcy's equation and stochastic advection-diffusion-dispersion equation
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Publication:618565
DOI10.1007/s10915-010-9346-5zbMath1203.65019OpenAlexW2070925045MaRDI QIDQ618565
Guang Lin, Alexandre M. Tartakovsky
Publication date: 16 January 2011
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10915-010-9346-5
Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Diffusion (76R50) Applications of stochastic analysis (to PDEs, etc.) (60H30) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Generation, random and stochastic difference and differential equations (37H10) Numerical solutions to stochastic differential and integral equations (65C30)
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Cites Work
- Unnamed Item
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- An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations
- Pseudo-spectral and asymptotic sensitivity investigation of counter- rotating vortices
- Adaptive sparse grid multilevel methods for elliptic PDEs based on finite differences
- Monomial cubature rules since ``Stroud: A compilation
- Dimension-adaptive tensor-product quadrature
- Finite elements for elliptic problems with stochastic coefficients
- On solving elliptic stochastic partial differential equations
- Efficient implementation of weighted ENO schemes
- Simple cubature formulas with high polynomial exactness
- Monomial cubature rules since ``Stroud: A compilation. II
- High dimensional polynomial interpolation on sparse grids
- Sparse grid collocation schemes for stochastic natural convection problems
- Sample function regularity for Gaussian processes with the parameter in a Hilbert space
- High dimensional integration of smooth functions over cubes
- Convergence study of the truncated Karhunen–Loeve expansion for simulation of stochastic processes
- Approximation Results for Orthogonal Polynomials in Sobolev Spaces
- Properties of Some Weighted Sobolev Spaces and Application to Spectral Approximations
- On Generating Orthogonal Polynomials
- On the Optimality of the Discrete Karhunen--Loève Expansion
- Eulerian Moment Equations for 2-D Stochastic Immiscible Flow
- Stochastic Solutions for the Two-Dimensional Advection-Diffusion Equation
- The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
- High-Order Collocation Methods for Differential Equations with Random Inputs
- Supersensitivity due to uncertain boundary conditions
