Anisotropic mesh adaptation for steady convection-dominated problems based on bubble-type local mesh generation

ABSTRACT

For convection–diffusion equations, it is difficult to obtain accurate solutions due to the presence of layers when convection dominates the diffusion. In this work, a new anisotropic adaptive meshing algorithm for convection-dominated problems is designed to optimize the mesh alignment, size and aspect ratio. Three main techniques are used. First, the streamline upwind Petrov–Galerkin (SUPG) method is used to stabilize the numerical scheme. Second, the a posteriori error estimator is computed and a new metric tensor is deduced. Third, optimal anisotropic meshes are generated by the anisotropic bubble-type local mesh generation (ABLMG) method. Compared with other mesh generation strategies, high-quality mesh can be obtained efficiently. Our algorithm is tested on several examples and the numerical results show that the algorithm is robust.

Keywords:

• Anisotropic mesh adaptation
• metric tensor
• convection-dominated problem
• stabilized finite element method
• local mesh generation

2010 AMS SUBJECT CLASSIFICATIONS:

• 65N50
• 65N30

Acknowledgments

We would like to thank the referees for their many valuable comments and suggestions, which have led to a significantly improved presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by the National Natural Science Foundation of China [nos. 11471262 and 11501450], China Postdoctoral Science Foundation [no. 2018M633568], Natural Science Basic Research Plan in Shaanxi Province of China [no. 2018JQ1049] and the Fundamental Research Funds for the Central Universities.