Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (3): 716-726.

• Articles • Previous Articles     Next Articles

A Optimal Uniformly Convergent Discontinuous Galerkin Finite Element Method for Singularly Perturbed Problem

 YANG Yu-Bo, ZHU Peng, YIN Yun-Hui   

  1. Nanhu College, Jiaxing University, Zhejiang Jiaxing 314001; School of Mathematics, Physics and Information, |Jiaxing University, Zhejiang Jiaxing 314001
  • Received:2012-12-16 Revised:2013-11-22 Online:2014-06-25 Published:2014-06-25
  • Supported by:

    浙江省自然科学基金(LQ12A01014)、 浙江省教育厅科研项目(Y201330020)和嘉兴学院科研启动基金(70510017)资助

Abstract:

A nonsymmetric discontinuous Galerkin finite element method with interior penalties is considered for one-dimensional
singularly perturbed convection-diffusion problem. On a Bakhvalov-Shishkin mesh with Lagrange linear elements, the method is shown to be convergent, uniformly in the perturbation parameter ε, of optimal error O(N-1) in the energy
norm, where N is the number of mesh. Finally, through numerical experiments, the authers verified the theoretical result.

Key words: Singularly perturbed problem, Discontinuous Galerkin finite element method, Bakhvalov-Shishkin mesh, Uniform convergence

CLC Number: 

  • 65N30
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