Streamline diffusion finite element method for stationary incompressible natural convection problem

Abstract

In this article, a streamline diffusion finite element method is proposed and analyzed for stationary incompressible natural convection problem (NC). This method is stable for any combinations of velocity, pressure, and temperature finite element spaces, without requiring inf-sup condition. The well-posedness and convergence (at optimal error rate) of this scheme are proved in terms of some conditions. Numerical experiments are illustrated to validate our theoretical analysis and show the streamline diffusion finite element approach is effective for solving the NC problems.

Acknowledgments

The authors are very grateful to the editor for their valuable comments and suggestions to help us further improve the quality of the paper and make us more serious in our future work.

Additional information

Funding

This work is in part supported by the Doctoral Scientific Research Foundation of Xinjiang University (No. BS150207, BS150211); NSF of China (No. 11671345, No. 61163027, No. 11701493 and No. 41501107).