Anisotropic mesh adaptation method based on anisotropic bubble-type local mesh generation

A new anisotropic adaptive mesh refinement method based on anisotropic bubble-type local mesh generation (ABLMG) for elliptic partial differential equations is proposed. The anisotropic meshes are generated as quasi-uniform meshes in metric spaces with the metric determined on each vertex by anisotropic a posteriori error estimator. Under the new metric, the error is equidistributed in the directions of maximum and minimum stretching on an element, and the mesh size is reduced/coarsend in regions with large/small errors. With the full use of the adjacent lists provided by the node placement method, the local mesh for each vertex is generated through ABLMG method. Compared with other methods, the mesh refining and coarsening can be obtained in the same framework and the mesh suits the metric well at each refinement level. Numerical results in two-dimensions are presented to verify the ability of our metric tensor to generate anisotropic mesh with correct concentration and stretching direction.