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

作者：Duan Huo Yuan; Hsieh Po Wen; Tan Roger C E; Yang Suh Yuh^*

来源：Computer Methods in Applied Mechanics and Engineering, 2012, 247: 15-36.

DOI：10.1016/j.cma.2012.07.018

• Reaction-convection-diffusion equation
• Boundary layer
• Interior layer
• Finite element method
• Stabilization method

In this paper, we propose and analyze a new stabilized finite element method using continuous piecewise linear (or bilinear) elements for solving 20 reaction-convection-diffusion equations. The equation under consideration involves a small diffusivity E and a large reaction coefficient a, leading to high Peclet number and high Damkohler number. In addition to giving error estimates of the approximations in L-2 and H-1 norms, we explicitly establish the dependence of error bounds on the diffusivity, the L-infinity 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 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.

• 出版日期2012
• 单位中央民族大学