國立清華大學 數學系

Abstract: In this talk, we will introduce a new stabilized finite element method using continuous piecewise linear (or bilinear) elements for the reaction-convection-diffusion equations. The equation under consideration involves a small diffusivity and a large reaction coefficient, leading to high Peclet number and high Damkohler number. 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 size of convection field, the reaction coefficient and the mesh size. Our analysis shows that the proposed method is particularly suitable for problems with a small diffusivity and a large reaction coefficient, or more precisely, with a large mesh Peclet number and a large mesh Damkohler number. Several numerical examples exhibiting boundary or interior layers are given to illustrate the high accuracy and stability of the proposed method. The results obtained are also compared with those of existing stabilization methods. This is joint work with Huo-Yuan Duan, Po-Wen Hsieh, and Roger C. E. Tan. Tea Time: 3:30PM R707