68 citations · 139 across the 15 of their papers we have counts for
17 papers
Stability, Convergence, and Error Analysis of Finite Element Methods for 3D Magnetohydrodynamics with -Laplacian Viscosity
Kim Ngan Le, Akash Ashirbad Panda, Evana Islam Sarkar
This paper develops a fully discrete finite element method for three-dimensional incompressible magnetohydrodynamic (MHD) flows with nonlinear -Laplace viscosity. The scheme com…
Numerical method and Error estimate for stochastic Landau--Lifshitz--Bloch equation
Beniamin Goldys, Chunxi Jiao, Kim-Ngan Le
We study numerical methods for solving a system of quasilinear stochastic partial differential equations known as the stochastic Landau-Lifshitz-Bloch (LLB) equation on a bounded d…
Existence, uniqueness and regularity of solutions to the stochastic Landau-Lifschitz-Slonczewski equation
Beniamin Goldys, Chunxi Jiao, Kim Ngan Le
In this paper we are concerned with the stochastic Landau-Lifshitz-Slonczewski equation (LLS) that describes magnetisation of an inifnite nanowire evolving under current driven spi…
Design and convergence analysis of numerical methods for stochastic evolution equations with Leray-Lions operator
Jerome Droniou, Beniamin Goldys, Kim-Ngan Le
*The gradient discretisation method (GDM) is a generic framework, covering many classical methods (Finite Elements, Finite Volumes, Discontinuous Galerkin, etc.), for designing and…
A semidiscrete finite element approximation of a time-fractional Fokker-Planck equation with nonsmooth initial data
Kim Ngan Le, William McLean, Kassem Mustapha
We present a new stability and convergence analysis for the spatial discretization of a time-fractional Fokker--Planck equation in a convex polyhedral domain, using continuous, pie…
Existence, uniqueness and regularity of the solution of the time-fractional Fokker-Planck equation with general forcing
Kim-Ngan Le, William McLean, Martin Stynes
A time-fractional Fokker-Planck initial-boundary value problem is considered, with differential operator ,…
Existence of a unique solution and invariant measures for the stochastic Landau--Lifshitz--Bloch equation
Zdzislaw Brzeźniak, Beniamin Goldys, Kim Ngan Le
The Landau--Lifshitz--Bloch equation perturbed by a space-dependent noise was proposed in Garanin 1991 as a model for evolution of spins in ferromagnatic materials at the full rang…
A combined GDM--ELLAM--MMOC scheme for advection dominated PDEs
Hanz Martin Cheng, Jérôme Droniou, Kim-Ngan Le
We propose a combination of the Eulerian Lagrangian Localised Adjoint Method (ELLAM) and the Modified Method of Characteristics (MMOC) for time-dependent advection-domina\-ted PDEs…
Convergence analysis of a family of ELLAM schemes for a fully coupled model of miscible displacement in porous media
Hanz Martin Cheng, Jerome Droniou, Kim-Ngan Le
We analyse the convergence of numerical schemes in the GDM-ELLAM (Gradient Discretisation Method-Eulerian Lagrangian Localised Adjoint Method) framework for a strongly coupled elli…
A finite element approximation for the stochastic Landau--Lifshitz--Gilbert equation with multi-dimensional noise
Beniamin Goldys, Joseph Grotowski, Kim-Ngan Le
We propose an unconditionally convergent linear finite element scheme for the stochastic Landau--Lifshitz--Gilbert (LLG) equation with multi-dimensional noise. By using the Doss-Su…
A finite element approximation for the stochastic Maxwell--Landau--Lifshitz--Gilbert system
Beniamin Goldys, Kim-Ngan Le, Thanh Tran
The stochastic Landau--Lifshitz--Gilbert (LLG) equation coupled with the Maxwell equations (the so called stochastic MLLG system) describes the creation of domain walls and vortice…
Weak solutions of the Landau--Lifshitz--Bloch equation
Kim Ngan Le
The Landau--Lifshitz--Bloch (LLB) equation is a formulation of dynamic micromagnetics valid at all temperatures, treating both the transverse and longitudinal relaxation components…
Finite element approximation of a time-fractional diffusion problem in a non-convex polygonal domain
Kim Ngan Le, William McLean, Bishnu Lamichhane
An initial-boundary value problem for the time-fractional diffusion equation is discretized in space using continuous piecewise-linear finite elements on a polygonal domain with a…
Numerical solution of the time-fractional Fokker-Planck equation with general forcing
Kim Ngan Le, William McLean, Kassem Mustapha
We study two schemes for a time-fractional Fokker-Planck equation with space- and time-dependent forcing in one space dimension. The first scheme is continuous in time and is discr…
A finite element approximation for the stochastic Landau-Lifshitz-Gilbert equation
Beniamin Goldys, Kim-Ngan Le, Thanh Tran
The stochastic Landau--Lifshitz--Gilbert (LLG) equation describes the behaviour of the magnetization under the influence of the effective field consisting of random fluctuations. W…
On a decoupled linear FEM integrator for Eddy-current-LLG
Kim-Ngan Le, Marcus Page, Dirk Praetorius +1
We propose a numerical integrator for the coupled system of the eddy-current equation with the nonlinear Landau-Lifshitz-Gilbert equation. The considered effective field contains a…
A convergent finite element approximation for the quasi-static Maxwell--Landau--Lifshitz--Gilbert equations
Kim-Ngan Le, T. Tran
We propose a -linear scheme for the numerical solution of the quasi-static Maxwell-Landau-Lifshitz-Gilbert (MLLG) equations. Despite the strong nonlinearity of the Landau-Lifshi…