A finite element variational multiscale method for steady-state natural convection problem based on two local gauss integrations

In this article, supposing that the velocity, pressure, and temperature are approximated by the elements P2-P1-P2, and applying the orthogonal projection technique, we introduce two Gauss integrations as a stabilizing term in the common variational multiscale (VMS) method and derive a new VMS (Two Gauss VMS) method for steady-state natural convection problem. Comparing with the common VMS method, the Two Gauss VMS method does not need to introduce any extra variable and reduces the degrees of freedom of the discrete system a lot, but gets the same stabilized result. The effectiveness and stability of the Two Gauss VMS method are further demonstrated through two numerical examples. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 361-375, 2014