I am interested in the development and analysis of finite element methods for nonlinear models in micromagnetics. A central goal is to design structure-preserving numerical schemes that are energy-stable, linear, and optimally convergent, supported by rigorous analysis. Some work in this direction includes:
Strong convergence of finite element schemes for the stochastic Landau–Lifshitz–Bloch equation. IMA J. Numerical Analysis (2026, to appear). arXiv:2602.18021.
Error analysis of scalar auxiliary variable finite element methods for the Landau–Lifshitz–Bloch equation. Computers and Mathematics with Applications, 217 (2026).
Numerical analysis of the Landau–Lifshitz–Bloch equation with spin-torques. ESAIM: Mathematical Modelling and Numerical Analysis, 60, no. 3 (2026).
(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, 60, no. 2 (2026).
(with T. Tran) Stable C^1-conforming finite element methods for a class of nonlinear fourth-order evolution equations. Computational and Applied Mathematics, 45, 426 (2026).
Energy-stable finite element approximation of the Landau–Lifshitz–Bloch equation below the Curie temperature. J. Scientific Computing 104 (2), Paper no. 50 (2025).
Mixed finite element methods for the Landau–Lifshitz–Baryakhtar and the regularised Landau–Lifshitz–Bloch equations in micromagnetics. J. Scientific Computing 103 (2), Paper no. 65 (2025).
As part of my research in micromagnetics, I also investigate the well-posedness and long-time behavior of the underlying (S)PDE models to support the analysis of numerical schemes. This theoretical foundation is crucial, as the regularity of the exact solution directly influences the convergence rate and stability of the numerical methods. Some research in this direction includes:
(with K. Le and T. Tran) The Landau–Lifshitz–Bloch equation on polytopal domains: Unique existence and finite element approximation. IMA J. Numerical Analysis, drag002 (2026).
(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, 104420 (2026).
(with B. Goldys and T. Tran) The stochastic Landau–Lifshitz–Baryakhtar equation: Global solution and invariant measure. J. Mathematical Analysis and Applications, 556, 130235 (2026).
(with T. Tran) Global solutions of the Landau–Lifshitz–Baryakhtar equation. J. Differential Equations 371, 191-230 (2023).
Computational tumour modelling seeks to capture coupled cell dynamics and nutrient transport, with the aim of informing optimal treatment strategies. Diffuse-interface (phase-field) models can describe tumour evolution through coupled PDEs that track volume fractions of tumour tissues and nutrients. I am interested in structure-preserving numerical methods to solve these problems. Some research work in this direction includes:
(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).
More recently, my research interests have expanded to include thermally coupled magnetohydrodynamics (MHD)-type equations, which arise in models of magnetised fluids under thermal and random influences. I am currently investigating the well-posedness of such stochastic partial differential equations (SPDEs) in the strong sense. Some ongoing work includes:
(with T. Tran) Strong solutions for a class of stochastic thermo-magneto-hydrodynamic-type systems with multiplicative noise, arXiv:2509.14490 (2025).
To complement the theoretical analysis above, I am interested in the development and analysis of structure-preserving numerical methods for MHD-type problems. These systems pose significant challenges due to their nonlinearities and multi-physics nature, which can amplify instabilities and complicate convergence analysis. The focus is on preserving important physical invariants. Some ongoing work in this direction includes:
Error analysis of a divergence-preserving mixed finite element scheme for the incompressible Hall-magnetohydrodynamic equation. arXiv:2605.01764 (2026).