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Morley-Wang-Xu element methods with penalty for a fourth order elliptic singular perturbation problem

  • Wenqing Wang
  • Xuehai Huang
  • Kai Tang
  • Ruiyue Zhou
Article
  • 61 Downloads

Abstract

Two Morley-Wang-Xu element methods with penalty for the fourth order elliptic singular perturbation problem are proposed in this paper, including the interior penalty Morley-Wang-Xu element method and the super penalty Morley-Wang-Xu element method. The key idea in designing these two methods is combining the Morley-Wang-Xu element and penalty formulation for the Laplace operator. Robust a priori error estimates are derived under minimal regularity assumptions on the exact solution by means of some established a posteriori error estimates. Finally, we present some numerical results to demonstrate the theoretical estimates.

Keywords

Fourth order singular perturbation problem Morley-Wang-Xu element Interior penalty method Super penalty method Error analysis 

Mathematics Subject Classification (2010)

65N30 65N15 35J40 35J35 

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Notes

Acknowledgments

The work of this author was supported by the NSFC Projects 11771338 and 11671304, Zhejiang Provincial Natural Science Foundation of China Projects LY17A010010, LY15A010015 and LY15A010016, and Wenzhou Science and Technology Plan Project G20160019.

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Authors and Affiliations

  1. 1.Department of Basic TeachingWenzhou Business CollegeWenzhouChina
  2. 2.College of Mathematics and Information ScienceWenzhou UniversityWenzhouChina

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