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A Dimension Splitting Generalized Interpolating Element-Free Galerkin Method for the Singularly Perturbed Steady Convection–Diffusion–Reaction Problems

Author

Listed:
  • Fengxin Sun

    (Faculty of Science, Ningbo University of Technology, Ningbo 315016, China)

  • Jufeng Wang

    (College of Finance & Information, Ningbo University of Finance & Economics, Ningbo 315175, China)

  • Xiang Kong

    (Faculty of Science, Ningbo University of Technology, Ningbo 315016, China)

  • Rongjun Cheng

    (Faculty of Maritime and Transportation, Ningbo University, Ningbo 315211, China)

Abstract

By introducing the dimension splitting method (DSM) into the generalized element-free Galerkin (GEFG) method, a dimension splitting generalized interpolating element-free Galerkin (DS-GIEFG) method is presented for analyzing the numerical solutions of the singularly perturbed steady convection–diffusion–reaction (CDR) problems. In the DS-GIEFG method, the DSM is used to divide the two-dimensional CDR problem into a series of lower-dimensional problems. The GEFG and the improved interpolated moving least squares (IIMLS) methods are used to obtain the discrete equations on the subdivision plane. Finally, the IIMLS method is applied to assemble the discrete equations of the entire problem. Some examples are solved to verify the effectiveness of the DS-GIEFG method. The numerical results show that the numerical solution converges to the analytical solution with the decrease in node spacing, and the DS-GIEFG method has high computational efficiency and accuracy.

Suggested Citation

  • Fengxin Sun & Jufeng Wang & Xiang Kong & Rongjun Cheng, 2021. "A Dimension Splitting Generalized Interpolating Element-Free Galerkin Method for the Singularly Perturbed Steady Convection–Diffusion–Reaction Problems," Mathematics, MDPI, vol. 9(19), pages 1-15, October.
  • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2524-:d:651626
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    References listed on IDEAS

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    1. Cheng, Jing, 2021. "Analysis of commercial land leasing of the district governments of Beijing in China," Land Use Policy, Elsevier, vol. 100(C).
    2. Jing Cheng, 2020. "Data Analysis of the Factors Influencing the Industrial Land Leasing in Shanghai Based on Mathematical Models," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-11, April.
    3. Jufeng Wang & Fengxin Sun & Ying Xu, 2020. "Research on Error Estimations of the Interpolating Boundary Element Free-Method for Two-Dimensional Potential Problems," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-10, July.
    4. Lin, Ji & Reutskiy, S.Y. & Lu, Jun, 2018. "A novel meshless method for fully nonlinear advection–diffusion-reaction problems to model transfer in anisotropic media," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 459-476.
    5. Cheng, Jing, 2020. "Analyzing the factors influencing the choice of the government on leasing different types of land uses: Evidence from Shanghai of China," Land Use Policy, Elsevier, vol. 90(C).
    6. Lin, Ji & Reutskiy, Sergiy, 2020. "A cubic B-spline semi-analytical algorithm for simulation of 3D steady-state convection-diffusion-reaction problems," Applied Mathematics and Computation, Elsevier, vol. 371(C).
    7. Nguyen, Vinh Phu & Rabczuk, Timon & Bordas, Stéphane & Duflot, Marc, 2008. "Meshless methods: A review and computer implementation aspects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 763-813.
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    Cited by:

    1. Yumin Cheng, 2022. "Preface to the Special Issue on “Numerical Computation, Data Analysis and Software in Mathematics and Engineering”," Mathematics, MDPI, vol. 10(13), pages 1-5, June.

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