Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
A multiscale finite element method for elliptic problems in composite materials and porous media
Journal of Computational Physics
A stochastic projection method for fluid flow. I: basic formulation
Journal of Computational Physics
Optimization by Vector Space Methods
Optimization by Vector Space Methods
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
Spectral Polynomial Chaos Solutions of the Stochastic Advection Equation
Journal of Scientific Computing
A stochastic projection method for fluid flow II.: random process
Journal of Computational Physics
Modeling uncertainty in flow simulations via generalized polynomial chaos
Journal of Computational Physics
Analysis of a Two-Scale, Locally Conservative Subgrid Upscaling for Elliptic Problems
SIAM Journal on Numerical Analysis
Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes
SIAM Journal on Scientific Computing
Using stochastic analysis to capture unstable equilibrium in natural convection
Journal of Computational Physics
Accurate multiscale finite element methods for two-phase flow simulations
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Evolution of Probability Distribution in Time for Solutions of Hyperbolic Equations
Journal of Scientific Computing
Journal of Computational Physics
A stochastic mixed finite element heterogeneous multiscale method for flow in porous media
Journal of Computational Physics
A Stochastic Mortar Mixed Finite Element Method for Flow in Porous Media with Multiple Rock Types
SIAM Journal on Scientific Computing
General purpose software for efficient uncertainty management of large finite element models
Finite Elements in Analysis and Design
Extended stochastic FEM for diffusion problems with uncertain material interfaces
Computational Mechanics
Hi-index | 31.47 |
A stochastic variational multiscale method with explicit subgrid modelling is provided for numerical solution of stochastic elliptic equations that arise while modelling diffusion in heterogeneous random media. The exact solution of the governing equations is split into two components: a coarse-scale solution that can be captured on a coarse mesh and a subgrid solution. A localized computational model for the subgrid solution is derived for a generalized trapezoidal time integration rule for the coarse-scale solution. The coarse-scale solution is then obtained by solving a modified coarse formulation that takes into account the subgrid model. The generalized polynomial chaos method combined with the finite element technique is used for the solution of equations resulting from the coarse formulation and subgrid models. Finally, various numerical examples are considered for evaluating the method.