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Analysis of the element-free Galerkin method with penalty for general second-order elliptic problems

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  • Zhang, Tao
  • Li, Xiaolin

Abstract

In this paper, an element-free Galerkin (EFG) method with penalty for solving general second-order elliptic problems with mixed boundary conditions is presented. A priori approximate estimations of the penalty method are obtained under some proper assumptions, which ensure the availability of the penalty method. By defining a special norm, the existence and uniqueness for the weak solution of the penalized continuous variational formula are proved, which guarantee the validity of the EFG discretization. Error estimates of the EFG method are provided in L2 and H1 norms for the Dirichlet and the mixed boundaries, respectively. Numerical examples are finally performed to illustrate the theoretical results.

Suggested Citation

  • Zhang, Tao & Li, Xiaolin, 2020. "Analysis of the element-free Galerkin method with penalty for general second-order elliptic problems," Applied Mathematics and Computation, Elsevier, vol. 380(C).
    • Handle: RePEc:eee:apmaco:v:380:y:2020:i:c:s0096300320302721
    DOI: 10.1016/j.amc.2020.125306
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    References listed on IDEAS

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    1. Li, Xiaolin & Dong, Haiyun, 2019. "Analysis of the element-free Galerkin method for Signorini problems," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 41-56.
    2. Li, Xiaolin & Chen, Hao & Wang, Yan, 2015. "Error analysis in Sobolev spaces for the improved moving least-square approximation and the improved element-free Galerkin method," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 56-78.
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    Cited by:

    1. Sun, Fengxin & Wang, Jufeng & Xu, Ying, 2024. "An improved stabilized element-free Galerkin method for solving steady Stokes flow problems," Applied Mathematics and Computation, Elsevier, vol. 463(C).
    2. Dehghan, Mehdi & Gharibi, Zeinab, 2021. "Numerical analysis of fully discrete energy stable weak Galerkin finite element Scheme for a coupled Cahn-Hilliard-Navier-Stokes phase-field model," Applied Mathematics and Computation, Elsevier, vol. 410(C).

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