Analysis of a new stabilized finite element method for the reactionconvectiondiffusion equations with a large reaction coefficient
In this paper, we propose and analyze a new stabilized finite element method using continuous piecewise linear (or bilinear) elements for solving 2D reactionconvectiondiffusion equations. The equation under consideration involves a small diffusivity ? ? and a large reaction coefficient ? ? , leading to high Pclet number and high Damkhler number. In addition to giving error estimates of the approximations in L2 L 2 and H1 H 1 norms, we explicitly establish the dependence of error bounds on the diffusivity, the L? L ? 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 Pclet number and a large mesh Damkhler 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.
finite element method reactionconvectiondiffusion equation interior layer stabilization method boundary layer