37 citations · 102 across the 10 of their papers we have counts for
4 papers · 1 filter
Causality and Bayesian network PDEs for multiscale representations of porous media
Kimoon Um, Eric Joseph Hall, Markos A. Katsoulakis +1
Microscopic (pore-scale) properties of porous media affect and often determine their macroscopic (continuum- or Darcy-scale) counterparts. Understanding the relationship between pr…
Uncertainty quantification for generalized Langevin dynamics
Eric Joseph Hall, Markos A. Katsoulakis, Luc Rey-Bellet
We present efficient finite difference estimators for goal-oriented sensitivity indices with applications to the generalized Langevin equation (GLE). In particular, we apply these…
Computable error estimates for finite element approximations of elliptic partial differential equations with rough stochastic data
Eric Joseph Hall, Håkon Hoel, Mattias Sandberg +2
We derive computable error estimates for finite element approximations of linear elliptic partial differential equations (PDE) with rough stochastic coefficients. In this setting,…
Higher order spatial approximations for degenerate parabolic stochastic partial differential equations
Eric Joseph Hall
We consider an implicit finite difference scheme on uniform grids in time and space for the Cauchy problem for a second order parabolic stochastic partial differential equation whe…