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

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.