一种新的求解对流占优问题的自适应网格细化方法

Numerical solutions on uniform meshes always exhibit spurious oscillations,especially near the layers when convection dominates the diffusion.To improve the stabilization and accuracy many stabilized finite element methods and adaptive mesh refinement schemes have been proposed.For convection-dominated problems,a new adaptive mesh refinement method based on bubble-type local mesh generation(BLMG)is developed.The streamline upwind Petrov-Galerkin(SUPG)method is used to stabilize the numerical scheme.To refine the mesh,the mesh size is defined and adjusted according to a posteriori error estimator.Finally optimal meshes are generated from the computed mesh size by the BLMG method in which the nodes are viewed as the centers of bubbles and move according to the Newton's second law of motion.Compared with other mesh generation strategies,the refining and coarsening can be obtained smoothly in the same framework and the updated triangles remain very well shaped at all levels of refinement.Our algorithm is tested on several examples and the numerical results show that the algorithm is robust.