FINITE ELEMENT ANALYSIS OF LINEARLY EXTRAPOLATED BLENDED BACKWARD DIFFERENCE FORMULA (BLEBDF) FOR THE NATURAL CONVECTION FLOWS

Abstract

In this paper, we study the stability and convergence of fully discrete finite element method with grad-div stabilization for the incompressible non-isothermal fluid flows. The proposed scheme uses finite element discretization in space and linearly extrapolated blended Backward Differentiation Formula (BLEBDF) in time. We prove the unconditional stability over finite time interval and optimally convergence of the scheme. We also present numerical experiments to verify our theoretical convergence rates and show the reliability of the scheme.

Keywords

• Finite Element Method
• Grad-div stabilization
• Natural Convection

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