A new stabilized finite element method for advection-diffusion-reaction equations

In this article, a new stabilized finite element method is proposed and analyzed for advection-diffusion-reaction equations. The key feature is that both the mesh-dependent Peclet number and the mesh-dependent Damkohler number are reasonably incorporated into the newly designed stabilization parameter. The error estimates are established, where, up to the regularity-norm of the exact solution, the explicit-dependence of the diffusivity, advection, reaction, and mesh size (or the dependence of the mesh-dependent Peclet number and the mesh-dependent Damkohler number) is revealed. Such dependence in the error bounds provides a mathematical justification on the effectiveness of the proposed method for any values of diffusivity, advection, dissipative reaction, and mesh size. Numerical results are presented to illustrate the performance of the method. (c) 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 616-645, 2016