My Research
My research interests include the modelling, analysis, and numerical approximation of fluid dynamic problems using finite element methods and projection methods. My ongoing project involves developing an algorithm to approximate the solution of incompressible Navier-Stokes equations and heat equation, and establishing its stability and space-time error convergence both theoretically and numerically.
Publications
[3]
An Vu and Loic Cappanera. "Stability and convergence of a semi-implicit projection scheme for multiphase incompressible Navier-Stokes equations and heat equation", under preparation.
[2]
An Vu and Loic Cappanera. "Error analysis for incompressible flows with variable density and viscosity", submitted.
[1]
S. Ingimarson, M. Neda, L. Rebholz, J. Reyes, and A. Vu, "Improved long time accuracy for projection methods for Navier-Stokes equations using EMAC formulation", International Journal of Numerical Analysis and Modeling, (2022) Volume 20, Number 2, Pages 176–198, DOI: 10.4208/ijnam2023-1008.
Conference Presentations
Finite Element Rodeo
March 8-9, 2024, Houston, TX
"Finite element methods for multiphase incompressible Navier-Stokes equations with thermal convection."
SIAM TX-LA
November 3-5, 2023, Lafayette, LA
"Semi-implicit projection methods for incompressible flows with variable density coupled with the temperature equation."
17th U. S. National Congress on Computational Mechanics
July 23-27, 2023, Albuquerque, NM
"Finite element methods for incompressible flows with variable density applied to thermodynamics."
Finite Element Rodeo
March 24-25, 2023, College Station, TX
"Finite element methods for incompressible flows with variable density applied to thermodynamics."
Texas Women in Math Symposium
March 4-5, 2023, Austin, TX
"Error estimates for semi-implicit time stepping scheme for incompressible Navier-Stokes equations with variable density."
SIAM TX-LA
November 4-6, 2022, Houston, TX
"Finite element methods for incompressible flows with variable density applied to thermodynamics."