Abstract
A new finite element variational multiscale (VMS) method based on two local Gauss integrations is proposed and analyzed for the stationary conduction‐convection problems. The valuable feature of our method is that the action of stabilization operators can be performed locally at the element level with minimal additional cost. The theory analysis shows that our method is stable and has a good precision. Finally, the numerical test agrees completely with the theoretical expectations and the “ exact solution,” which show that our method is highly efficient for the stationary conduction‐convection problems.
Highlights
The conduction-convection problems constitute an important system of equations in atmospheric dynamics and dissipative nonlinear system of equations
Christon et al 10 summarized some relevant results for the fluid dynamics of thermally driven cavity
Our VMS finite element method based on two local Gauss integrations and εd 0.1 h is suitable for the Sobolev space
Summary
The conduction-convection problems constitute an important system of equations in atmospheric dynamics and dissipative nonlinear system of equations. A multigrid MG technique was applied for the conduction-convection problems 11,. In 3 , an analysis of conduction natural convection conjugate heat transfer in the gap between concentric cylinders under solar irradiation was carried out. In , Boland and Layton gave an error analysis for finite element methods for steady natural convection problems. The new finite element VMS strategy requires edge-based data structure and a subdivision of grids into patches. For the conduction-convection problems, we establish such system that Ω be a bounded domain in Rd d 2 or 3 , with Lipschitz-continuous boundary ∂Ω. We consider the stationary conduction-convection problem as follows:. The finite element VMS method is given.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
