Kim-Ngan Le

Numerical Solution of the Time-Fractional Fokker--Planck Equation with General Forcing

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 discretized in space using a piecewise-linear Galerkin finite element method. The second is continuous in space and employs a time-stepping procedure similar to the classical implicit Euler method. We show that the space discretization is second-order accurate in the spatial

On a decoupled linear FEM integrator for eddy-current-LLG

L_2

Convergence analysis of a family of ELLAM schemes for a fully coupled model of miscible displacement in porous media

-norm, uniformly in time, whereas the corresponding error for the time-stepping scheme is

Finite element approximation of a time-fractional diffusion problem in a non-convex polygonal domain

O(k^\alpha)

A convergent finite element approximation for the quasi-static Maxwell-Landau-Lifshitz-Gilbert equations

for a uniform time step

A finite element approximation for the stochastic Landau–Lifshitz–Gilbert equation

k

Finite element approximation of a time-fractional diffusion problem for a domain with a re-entrant corner

, where

Weak solutions of the Landau–Lifshitz–Bloch equation☆

\alpha\in(1/2,1)

A finite element approximation for the quasi-static Maxwell--Landau--Lifshitz--Gilbert equations

is the fractional diffusion parameter. In numerical experiments using a combined, fully-discrete method, we observe convergence behaviour consistent with these results.

A combined GDM--ELLAM--MMOC scheme for advection dominated PDEs

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 general field contribution, and we particularly cover exchange, anisotropy, applied field and magnetic field (stemming from the eddy-current equation). Even though the considered problem is nonlinear, our scheme requires only the solution of two linear systems per time-step. Moreover, our algorithm decouples both equations so that in each time-step, one linear system is solved for the magnetization, and afterwards one linear system is solved for the magnetic field. Unconditional convergence – at least of a subsequence – towards a weak solution is proved, and our analysis even provides existence of such weak solutions. Numerical experiments with micromagnetic benchmark problems underline the performance and the stability of the proposed algorithm.