Finite element analysis of linearly extrapolated blended backward difference formula (BLEBDF) for the natural convection flows

This thesis proposes and studies a fully discrete finite element method with grad-div stabilization for the incompressible non-isothermal fluid flows. The proposed algorithm uses finite element discretization in space and linearly extrapolated blended Backward Differentiation Formula (BLEBDF) in time. The algorithm's solutions are unconditionally stable over finite time interval and optimally convergence to the true solutions both in time and space. Numerical experiments verify the theoretical convergence rates and test the reliability of the scheme on Marsigli's experiment.