8 papers
Error analysis of a divergence-preserving mixed finite element scheme for the incompressible Hall--magnetohydrodynamic equations
Beniamin Goldys, Agus L. Soenjaya, Thanh Tran
The incompressible Hall-magnetohydrodynamics (Hall--MHD) system presents substantial analytical and computational challenges due to its stiff, highly nonlinear Hall term and the st…
A mixed finite element method for a class of fourth-order stochastic evolution equations with multiplicative noise
Beniamin Goldys, Agus L. Soenjaya, Thanh Tran
We develop a fully discrete, semi-implicit mixed finite element method for approximating solutions to a class of fourth-order stochastic partial differential equations (SPDEs) with…
The Landau--Lifshitz--Bloch equation on polytopal domains: Unique existence and finite element approximation
Kim-Ngan Le, Agus L. Soenjaya, Thanh Tran
The Landau--Lifshitz--Bloch equation (LLBE) describes the evolution of the magnetic spin field in ferromagnets at high temperatures. In this paper, we study the numerical approxima…
Strong pathwise solutions for a class of stochastic thermo-magneto-hydrodynamic-type systems with multiplicative noise
Agus L. Soenjaya, Thanh Tran
We establish the existence and uniqueness of strong solutions, in both the PDE and probabilistic sense, for a broad class of nonlinear stochastic partial differential equations (SP…
The stochastic Landau--Lifshitz--Baryakhtar equation: Global solution and invariant measure
Beniamin Goldys, Agus L. Soenjaya, Thanh Tran
The Landau--Lifshitz--Baryakhtar (LLBar) equation perturbed by both additive and multiplicative noises is a system of fourth order stochastic PDEs which models the evolution of mag…
Error analysis of a fully discrete structure-preserving finite element scheme for a diffuse-interface model of tumour growth
Agus L. Soenjaya, Ping Lin, Thanh Tran
We develop a linear fully discrete structure-preserving finite element method for a diffuse-interface model of tumour growth. The system couples a Cahn--Hilliard type equation with…