5 citations · 5 across the 7 of their papers we have counts for
8 papers · 1 filter
Bayesian inference calibration of the modulus of elasticity
J. Dick, Q. T. Le Gia, K. Mustapha
This work uses the Bayesian inference technique to infer the Young modulus from the stochastic linear elasticity equation. The Young modulus is modeled by a finite Karhunen Loéve e…
A decomposition-based robust training of physics-informed neural networks for nearly incompressible linear elasticity
Josef Dick, Seungchan Ko, Quoc Thong Le Gia +2
Due to divergence instability, the accuracy of low-order conforming finite element methods for nearly incompressible elasticity equations deteriorates as the Lamé coefficient $λ\to…
Time-fractional diffusion equations with randomness, and efficient numerical estimations of expected values
Josef Dick, Hecong Gao, William McLean +1
In this work, we explore a time-fractional diffusion equation of order with a stochastic diffusivity parameter. We focus on efficient estimation of the expected values…
A simple modification to mitigate locking in conforming FEM for nearly incompressible elasticity
K. Mustapha, W. McLean, J. Dick +1
Due to the divergence-instability, the accuracy of low-order conforming finite element methods (FEMs) for nearly incompressible elasticity equations deteriorates as the Lamé parame…
High-order QMC nonconforming FEMs for nearly incompressible planar stochastic elasticity equations
J. Dick, T. Le Gia, W. McLean +2
In a recent work (Dick et al, arXiv:2310.06187), we considered a linear stochastic elasticity equation with random Lamé parameters which are parameterized by a countably infinite n…
An -robust and second-order accurate scheme for a subdiffusion equation
Kassem Mustapha, William McLean, Josef Dick
We investigate a second-order accurate time-stepping scheme for solving a time-fractional diffusion equation with a Caputo derivative of order~. The basic idea of our s…
Sparse grid approximation of nonlinear SPDEs: The Landau--Lifshitz--Gilbert equation
Xin An, Josef Dick, Michael Feischl +2
We show convergence rates for a sparse grid approximation of the distribution of solutions of the stochastic Landau-Lifshitz-Gilbert equation. Beyond being a frequently studied equ…
Quasi-Monte Carlo sparse grid Galerkin finite element methods for linear elasticity equations with uncertainties
M. Clarke, J. Dick, Q. T. Le Gia +2
We explore a linear inhomogeneous elasticity equation with random Lamé parameters. The latter are parameterized by a countably infinite number of terms in separated expansions. The…