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

Huo Yuan Duan, Po Wen Hsieh, Roger C.E. Tan, Suh Yuh Yang

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

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 ε and a large reaction coefficient σ, leading to high Péclet number and high Damköhler 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 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 Péclet number and a large mesh Damköhler 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.

Original languageEnglish
Pages (from-to)15-36
Number of pages22
JournalComputer Methods in Applied Mechanics and Engineering
Volume247-248
DOIs
StatePublished - 1 Nov 2012

Keywords

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

Fingerprint

Dive into the research topics of 'Analysis of a new stabilized finite element method for the reaction-convection-diffusion equations with a large reaction coefficient'. Together they form a unique fingerprint.

Cite this