Analysis of a new stabilized finite element method for the reaction-convection-diffusion equations with a large reaction coefficient

详细信息    查看全文

• 作者：Huo-Yuan Duan ; Po-Wen Hsieh ; Roger C.E. Tan ; Suh-Yuh Yang
• 关键词：Reaction&ndash ; convection&ndash ; diffusion equation ; Boundary layer ; Interior layer ; Finite element method ; Stabilization method
• 刊名：Computer Methods in Applied Mechanics and Engineering
• 出版年：2012
• 出版时间：1 November, 2012
• 年：2012
• 卷：247-248
• 期：Complete
• 页码：15-36
• 全文大小：6981 K

文摘

In this paper, we propose and analyze a new stabilized finite element method using continuous piecewise linear (or bilinear) elements for solving 2D reaction-convection-diffusion equations. The equation under consideration involves a small diffusivity and a large reaction coefficient , leading to high P¨¦clet number and high Damk?hler number. In addition to giving error estimates of the approximations in and norms, we explicitly establish the dependence of error bounds on the diffusivity, the norm 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 P¨¦clet number and a large mesh Damk?hler 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.