演講訊息 TALKS

We propose and analyze two new stabilized FEMs for solving boundary and interior layer problems. The first one is the bubble-stabilized LSFEM which is applied to solve scalar convection-dominated convection-diffusion problems. This bubble-stabilized LSFEM not only inherits the advantages of the primitive LSFEM, such as the resulting linear system being symmetric and positive definite, but also exhibits the characteristics of the residual-free bubble method without involving any stabilization parameters. Numerical experiments are given to demonstrate the effectiveness of the proposed bubble-stabilized LSFEM. The accuracy and computational cost of this method are also compared with those of the primitive LSFEM. We find that for a small diffusivity, the bubble-stabilized LSFEM is much better able to capture the nature of layer structure in the solution than the primitive LSFEM, even if the primitive LSFEM uses a very fine mesh or higher-order elements. The second method is a stabilized FEM in the Galerkin formulation. We analyze the method using continuous piecewise linear elements for reaction-convection-diffusion equations. The equation under consideration is reaction-convection-dominated, involving a small diffusivity and a large reaction coefficient. In addition to giving error estimates of the approximations in L2 and H1 norms, we explicitly establish the dependence of error bounds on the diffusivity, the module of convection field, the reaction coefficient and the mesh size. Several numerical examples exhibiting boundary layers are given to illustrate the high accuracy and stability of the newly proposed stabilized FEM. The results obtained are also compared with those of existing stabilized FEMs.