Research interests

• Numerical analysis for deterministic and stochastic PDEs.

• Computational electromagnetics.

• Fast solvers, iterative methods and neural networks, and high dimensional computation.

• Probability.

Publications/Preprints

1.   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)

2. 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)

3. X. Feng, L. Vo,  Analysis of Chorin-type projection methods for the stochastic Stokes equations with general multiplicative noise. Stoch PDE: Anal Comp. https://doi.org/10.1007/s40072-021-00228-4 . (2022)

4. 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)

5. 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)

6. 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). 

7.  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. Accepted. Communications in Computational Physics (2023). 

8. L. Vo, High moment and pathwise error estimates for fully discrete mixed finite element approximations of the stochastic Stokes equations with multiplicative noise. Submitted. (2023)

9. D. Nicholls, L. Vo, A High-Order Perturbation of Envelopes (HOPE) Method for Vector Electromagnetic Scattering by Periodic Inhomogeneous Media: Joint Analyticity. Submitted. (2023 )

10. D. Nicholls, L. Vo, An analytic continuation for the high-order perturbation of envelopes (HOPE) method for vector electromagnetic scattering by periodic inhomogeneous media. Submitted. (2024)

11. X. Feng, Y. Li, L. Vo, An optimal time discretization method for a class of semilinear stochastic wave equations with multiplicative noise. 2024. In preparation.

12. L. Vo, Analysis of fully discrete Crank-Nicolson finite element methods for a stochastic Keller-Segel chemotaxis system with gradient-type multiplicative noise}, 2024. In preparation.

13. X. Feng, L. Vo, Strong error estimates for fully discrete mixed finite element approximations of the stochastic Navier-Stokes equations with multiplicative noise, 2024. In preparation.

Projects

1. X. Chen, C. Ouyang and L. Vo, Large deviation of stochastic parabolic Anderson equation.

2. X. Feng and L. Vo,  Strong rate of convergence of mixed finite element method for the incompressible stochastic Navier-Stokes equations with multiplicative noise. 

3. X. Feng, L. Vo, Rates of convergence of finite element approximations of the 2D stochastic total variation flow with multiplicative noise. In preparation.

4. Y. Li and L. Vo, High-order time discretization method for stochastic nonlinear PDEs.

5. D. Nicholls and L. Vo, High order perturbation of envelopes methods for scattering grating problems.

6. L. Vo, Finite element method for stochastic logarithmic Schrodinger equation with multiplicative noise.