Agus L. Soenjaya

a.soenjaya@unsw.edu.au

PhD candidate, Mathematics

School of Mathematics and Statistics

UNSW Sydney

Research interests

Hi! I'm Agus, a final-year PhD student in the department of Applied Mathematics at UNSW, supervised by Prof. Thanh Tran (UNSW) and Prof. Ben Goldys (Univ. Sydney).

My PhD research explores how complex physical systems evolve over time, from the motion of magnetic materials and mixtures of fluids to the behaviour of conducting plasmas. These processes are often described by partial differential equations (PDEs), and in many cases, they are influenced by random effects, such as thermal fluctuations or microscopic noise. To capture this uncertainty, I work with stochastic PDEs (SPDEs), which combine the laws of physics with randomness.

My research focuses on developing and analysing stable and structure-preserving finite element methods: computational methods that not only approximate solutions to PDEs or SPDEs accurately but also respect the underlying physical laws, such as conservation of energy or mass. This allows simulations to remain faithful to the true behaviour of the system.

Currently, I am particularly interested in the Cahn–Hilliard-type equations (modelling phase separation in materials and tumour growth), the Landau–Lifshitz–Bloch equation (describing magnetisation dynamics at high temperatures), and the magnetohydrodynamics (MHD) equations (governing interaction between plasmas and magnetic fields).

Publications

Some recent publications are listed here. Click on the link to access the paper.

Strong convergence of finite element schemes for the stochastic Landau–Lifshitz–Bloch equation, IMA J. Numerical Analysis (2026, to appear). arXiv:2602.18021.
Numerical analysis of the Landau-Lifshitz-Bloch equation with spin-torques, ESAIM: Mathematical Modelling and Numerical Analysis (2026, to appear). arXiv:2502.20098.
(with B. Goldys and T. Tran) A mixed finite element method for a class of fourth-order stochastic evolution equations with multiplicative noise, ESAIM: Mathematical Modelling and Numerical Analysis (2026, to appear). arXiv:2505.04866.
(with K. Le and T. Tran) The Landau-Lifshitz-Bloch equation in polytopal domains: Unique existence and finite element approximation, IMA J. Numerical Analysis (2026, to appear). arXiv:2406.05808.
The Landau–Lifshitz–Bloch equation with spin diffusion: Global strong solution and finite element approximation. Numerical Methods for Partial Differential Equations, 42, no. 1 (2026): e70070.
(with B. Goldys and T. Tran) The stochastic Landau–Lifshitz–Baryakhtar equation: Global solution and invariant measure. J. Mathematical Analysis and Applications, 556 (2026), 130235.
(with B. Goldys and T. Tran) Global attractor and robust exponential attractors for some classes of fourth-order nonlinear evolution equations. Nonlinear Analysis: Real World Applications, 87 (2026), 104420.
Energy-stable finite element approximation of the Landau-Lifshitz-Bloch equation below the Curie temperature. J. Scientific Computing, 104 (2025), Paper no. 50.
Mixed finite element methods for the Landau–Lifshitz–Baryakhtar and the regularised Landau-Lifshitz-Bloch equations in micromagnetics. J. Scientific Computing, 103 (2025), Paper no. 65.
(with T. Tran) Global solutions of the Landau-Lifshitz-Baryakhtar equation. J. Differential Equations, 371 (2023), 191-230.

Recent preprints

Some recent preprints are listed here. A complete list can be found under 'CV' tab. Click on the link to access the preprint (or send me an e-mail if no link is available yet!).

Error analysis of a structure-preserving mixed finite element scheme for the incompressible Hall-MHD equation. Preprint (2026).
Error analysis of scalar auxiliary variable finite element methods for the Landau--Lifshitz--Bloch equation. arXiv:2603.02463 (2026).
(with P. Lin and T. Tran) Error analysis of a fully discrete structure-preserving finite element scheme for a diffuse-interface model of tumour growth. arXiv:2509.14486 (2025).
(with T. Tran) Strong solutions for a class of stochastic thermo-magneto-hydrodynamic-type systems with multiplicative noise. arXiv:2509.14490 (2025).

Work in progress

Some work in progress - these will be completed soon!

Structure-preserving finite element scheme for the Landau–Lifshitz–Bloch equation at any temperatures (2026).

NEWS:

6 March 2026: I finally submitted my PhD thesis for examination!
9 December 2025: I'm presenting at the Computational Mathematics and Stochastic Differential Equations special sessions of the AustMS Meeting 2025 at La Trobe University.
22 September 2025: I'm attending a special topic school on Optimality of adaptive finite element methods organised by the Hausdorff School for Mathematics at the University of Bonn. I'm also visiting Prof. Michael Feischl at TU Wien to work on a project related to structure-preserving FEM for the fully nonlinear Landau-Lifshitz-Bloch equation.
24 June 2025: I'm presenting at the 30th Biennial Numerical Analysis Conference organised by the University of Strathclyde, Glasgow. My talk will be on Finite element approximations of a micromagnetic model at elevated temperatures. The slides can be found here.
I'm also visiting Prof. Ping Lin at the University of Dundee to complete a project on structure-preserving FEM for a diffuse-interface model of tumour growth.
3 June 2025: I'm giving a talk in the department reading seminar series on (S)PDEs. My talk is on some research progress in the Well-posedness of the stochastic MHD equations.
1 April 2025: I'm giving a talk in the department reading seminar series on (S)PDEs. My talk is on Well-posedness of magnetohydrodynamics (MHD) equations. The slides can be found here.
10 December 2024: I'm giving a talk in the Computational Mathematics special session of NZMS, AMS, and AustMS joint meeting at the University of Auckland. The title of the talk is Finite element method for a micromagnetic model at elevated temperatures, and the slides can be found here.

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