Finite Element Method for Fluid Flow and

Solving convection-dominated phenomena using finite element method (FEM), including convection-diffusion equation, Navier-Stokes, equation for incompressible viscous flows, and nonlinear fluid-structure interactions (FSI). Foundational concepts of FEM include function spaces, strong and weak forms, Galerkin FEM, isoparametric discretization, stability analysis, and error estimates. Mixed FEM for Stokes flow, incompressibility and inf-sup conditions. Stabilization approaches, including residue-based variational multiscale methods. Arbitrary Lagrangian-Eulerian (ALE) formulation for nonlinear FSI, and selected advanced topics of research interest.