External Grants

National Science Foundation (Sole PI) 09/2025 - Present. Award number: DMS 2530211

Project title: Strong convergence of numerical methods for solving nonlinear stochastic PDEs.

National Science Foundation REU (Senior Personnel) 12/2025 - Present. Award number: DMS 2447683

Project title: UT Rio Grande Valley REU Program on Applied Mathematics and Computational and Data Science (AMCADS).

Preprints/submitted

H. D. Nguyen and L. Vo, Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise. Submitted (2025).
X. Feng and L. Vo, Full moment error estimates in strong norms for numerical approximations of stochastic Navier-Stokes equations with multiplicative noise, Part I: time discretization. Submitted (2025).
L. Vo, Analysis of fully discrete Crank-Nicolson finite element methods for a stochastic Keller-Segel chemotaxis system with gradient-type multiplicative noise. Submitted (2025).
X. Feng, Y. Li, and L. Vo, Optimal Order Space-Time Discretizations for the Nonlinear Stochastic Elastic Wave Equations with Multiplicative Noise. Submitted (2025).
X. Feng, Y. Li, and L. Vo, Optimal time discretization methods for a class of semilinear stochastic wave equations with multiplicative noise. Under revision. (2024).
L. Vo, Fully discrete mixed finite element methods for a stochastic Boussinesq system with multiplicative noise, 2025. In preparation.

Publications/Accepted

L. Vo, High moment and pathwise error estimates for fully discrete mixed finite element approximations of the stochastic Stokes equations with multiplicative noise. ESIAM: Mathematical Modelling and Numerical Analysis. https://doi.org/10.1051/m2an/2025030, Volume 59, Number 3, (2025).
D. Nicholls, L. Vo, A High-Order Perturbation of Envelopes (HOPE) Method for Vector Electromagnetic Scattering by Periodic Inhomogeneous Media: Analytic Continuation. Journal of Differential Equations, https://doi.org/10.1016/j.jde.2024.12.008, Volume 422, 106-151 (2025).
D. Nicholls, L. Vo, A High-Order Perturbation of Envelopes (HOPE) Method for Vector Electromagnetic Scattering by Periodic Inhomogeneous Media: Joint Analyticity. SIAM Journal on Applied Mathematics, https://doi.org/10.1137/24M1643189 (2025).
X. Feng, L. Vo, High moment and pathwise error estimates for fully discrete mixed finite element approximation of stochastic Navier-Stokes equations with additive noise. Communications in Computational Physics. DOI: 10.4208/cicp.OA-2023-0234, 36 (2024), pp. 821-849.
L. Vo, Higher order time discretization method for the stochastic Stokes equations with multiplicative noise. Journal of Scientific Computing. https://doi.org/10.1007/s10915-023-02375-3. (2023).
Y. Li, L. Vo, and G. Wang, Higher order time discretization method for a class of semilinear stochastic partial differential equations with multiplicative noise. Journal of Computational and Applied Mathematics. https://doi.org/10.1016/j.cam.2023.115442. (2023)
X. Feng, Y. Luo, L. Vo, and Z. Wang, An Efficient Iterative Method for Solving Parameter-Dependent and Random Convection–Diffusion Problems. Journal of Scientific Computing. https://doi.org/10.1007/s10915-021-01737-z . (2022)
X. Feng, L. Vo, Analysis of Chorin-type projection methods for the stochastic Stokes equations with general multiplicative noise. Stochastic and PDEs: Analysis and Computations. https://doi.org/10.1007/s40072-021-00228-4 . (2022)
X. Feng, A. Prohl, L. Vo, Optimally convergent mixed finite element methods for the stochastic Stokes equations, IMA Journal of Numerical Analysis; drab006, https://doi.org/10.1093/imanum/drab006 . (2021)
L. Vo, L. Hadji, Weakly Nonlinear Convection Induced by the Sequestration of CO2 in a Perfectly Impervious Geological Formation. Physics of Fluids 29(12):127101 DOI10.1063/1.4998253. (2017)

Projects

X. Feng and L. Vo, Strong rate of convergence of mixed finite element method for the incompressible stochastic Navier-Stokes equations with multiplicative noise.
L. Vo, Rates of convergence of finite element approximations of stochastic Keller-Segel systems and applications.
Y. Li and L. Vo, High-order time discretization method for stochastic nonlinear PDEs.
D. Nicholls and L. Vo, High-order perturbation of envelopes methods for scattering grating problems.
L. Vo, Finite element method for stochastic cubic Schrodinger equation with multiplicative noise.