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An analysis of the weak Galerkin finite element method for convection–diffusion equations

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  • Zhang, Tie
  • Chen, Yanli

Abstract

We study the weak finite element method solving convection–diffusion equations. A new weak finite element scheme is presented based on a special variational form. The optimal order error estimates are derived in the discrete H1-norm, the L2-norm and the L∞-norm, respectively. In particular, the H1-superconvergence of order k+2 is obtained under certain condition if polynomial pair Pk(K)×Pk+1(∂K) is used in the weak finite element space. Finally, numerical examples are provided to illustrate our theoretical analysis.

Suggested Citation

  • Zhang, Tie & Chen, Yanli, 2019. "An analysis of the weak Galerkin finite element method for convection–diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 612-621.
    • Handle: RePEc:eee:apmaco:v:346:y:2019:i:c:p:612-621
    DOI: 10.1016/j.amc.2018.10.064
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    Cited by:

    1. 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).
    2. Li, Wenjuan & Gao, Fuzheng & Cui, Jintao, 2024. "A weak Galerkin finite element method for nonlinear convection-diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 461(C).
    3. Qi, Wenya & Song, Lunji, 2020. "Weak Galerkin method with implicit θ-schemes for second-order parabolic problems," Applied Mathematics and Computation, Elsevier, vol. 366(C).

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