Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
A multiscale finite element method for elliptic problems in composite materials and porous media
Journal of Computational Physics
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
Modeling uncertainty in flow simulations via generalized polynomial chaos
Journal of Computational Physics
A variational multiscale finite element method for multiphase flow in porous media
Finite Elements in Analysis and Design - Special issue: The sixteenth annual Robert J. Melosh competition
High-Order Collocation Methods for Differential Equations with Random Inputs
SIAM Journal on Scientific Computing
An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
Journal of Computational Physics
Subgrid Upscaling and Mixed Multiscale Finite Elements
SIAM Journal on Numerical Analysis
Accurate multiscale finite element methods for two-phase flow simulations
Journal of Computational Physics
Sparse grid collocation schemes for stochastic natural convection problems
Journal of Computational Physics
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
SIAM Journal on Numerical Analysis
A non-linear dimension reduction methodology for generating data-driven stochastic input models
Journal of Computational Physics
Journal of Computational Physics
Geodesic entropic graphs for dimension and entropy estimation in manifold learning
IEEE Transactions on Signal Processing
Journal of Computational Physics
A stochastic mixed finite element heterogeneous multiscale method for flow in porous media
Journal of Computational Physics
Hi-index | 31.46 |
Flow through porous media is ubiquitous, occurring from large geological scales down to the microscopic scales. Several critical engineering phenomena like contaminant spread, nuclear waste disposal and oil recovery rely on accurate analysis and prediction of these multiscale phenomena. Such analysis is complicated by inherent uncertainties as well as the limited information available to characterize the system. Any realistic modeling of these transport phenomena has to resolve two key issues: (i) the multi-length scale variations in permeability that these systems exhibit, and (ii) the inherently limited information available to quantify these property variations that necessitates posing these phenomena as stochastic processes. A stochastic variational multiscale formulation is developed to incorporate uncertain multiscale features. A stochastic analogue to a mixed multiscale finite element framework is used to formulate the physical stochastic multiscale process. Recent developments in linear and non-linear model reduction techniques are used to convert the limited information available about the permeability variation into a viable stochastic input model. An adaptive sparse grid collocation strategy is used to efficiently solve the resulting stochastic partial differential equations (SPDEs). The framework is applied to analyze flow through random heterogeneous media when only limited statistics about the permeability variation are given.