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Convergence and supercloseness of a finite element method for a two-parameter singularly perturbed problem on Shishkin triangular mesh

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  • Lv, Yanhui
  • Zhang, Jin

Abstract

We consider a singularly perturbed elliptic problem with two parameters in two dimensions. Using linear finite element method on a Shishkin triangular mesh, we prove the uniform convergence and supercloseness in an energy norm. Some integral inequalities play an important role in our analysis. Numerical tests verify our theoretical results.

Suggested Citation

  • Lv, Yanhui & Zhang, Jin, 2022. "Convergence and supercloseness of a finite element method for a two-parameter singularly perturbed problem on Shishkin triangular mesh," Applied Mathematics and Computation, Elsevier, vol. 416(C).
    • Handle: RePEc:eee:apmaco:v:416:y:2022:i:c:s0096300321008353
    DOI: 10.1016/j.amc.2021.126753
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    References listed on IDEAS

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    1. Shenglan Xie & Huonian Tu & Peng Zhu, 2014. "Supercloseness Result of Higher Order FEM/LDG Coupled Method for Solving Singularly Perturbed Problem on S-Type Mesh," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-11, June.
    2. Zhang, Jin & Lv, Yanhui, 2021. "High-order finite element method on a Bakhvalov-type mesh for a singularly perturbed convection–diffusion problem with two parameters," Applied Mathematics and Computation, Elsevier, vol. 397(C).
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