Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1

Chinese Journal of Engineering Mathematics ›› 2016, Vol. 33 ›› Issue (3): 309-318.doi: 10.3969/j.issn.1005-3085.2016.03.009

Previous Articles     Next Articles

A Balanced Finite Element Method of Least-squares Formulation for Singularly Perturbed Reaction-diffusion Problems

QIU Chang-xin,  ZHAO Wei-jia,  SONG Li-na   

  1. School of Mathematics and Statistics, Qingdao University, Qingdao 266071
  • Received:2015-03-19 Accepted:2015-09-10 Online:2016-06-15 Published:2016-08-15
  • Supported by:
    The National Natural Science Foundation of China (11401332; 11072120).

Abstract:

For a kind of the singularly perturbed reaction-diffusion problem, the standard energy norm is too weak to measure adequately the errors of solutions computed by finite element methods. The multiplier of this problem gives an unbalanced norm whose different components have different orders of convergence. In the paper, we introduce a new stronger norm, construct the least-squares finite element method (LSFEM) in this new norm and develop a robust and stable numerical approach for more general singularly perturbed reaction-diffusion problems in 1D spaces. At last, numerical examples are presented to illustrate the proposed method and theoretical results.

Key words: singularly perturbed reaction-diffusion problem, least-squares methods, error estimates, finite element method

CLC Number: