A New Variational Multiscale FEM for the Steady-State Natural Convection Problem with Bubble Stabilization

Abstract

In this paper, a new variational multiscale finite element method (FEM) with bubble stabilization for the steady-state natural convection problem is presented. The new variational multiscale FEM is derived by using a decoupling and linear technique. Compared with the common projection-based stabilized FEM, the new method does not need to introduce any extra degree of freedom. Moreover, the new method has the same convergence precision as the standard Galerkin FEM. Finally, some numerical examples are given to show that the new method is efficient, reliable, and can save a lot of CPU-time for this problem.