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The Improved Element-Free Galerkin Method for 3D Steady Convection-Diffusion-Reaction Problems with Variable Coefficients

Author

Listed:
  • Heng Cheng

    (School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, China)

  • Zebin Xing

    (School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, China)

  • Yan Liu

    (School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, China)

Abstract

In order to obtain the numerical results of 3D convection-diffusion-reaction problems with variable coefficients efficiently, we select the improved element-free Galerkin (IEFG) method instead of the traditional element-free Galerkin (EFG) method by using the improved moving least-squares (MLS) approximation to obtain the shape function. For the governing equation of 3D convection-diffusion-reaction problems, we can derive the corresponding equivalent functional; then, the essential boundary conditions are imposed by applying the penalty method; thus, the equivalent integral weak form is obtained. By introducing the IMLS approximation, we can derive the final solved linear equations of the convection-diffusion-reaction problem. In numerical examples, the scale parameter and the penalty factor of the IEFG method for such problems are discussed, the convergence is proved numerically, and the calculation efficiency of the IEFG method are verified by four numerical examples.

Suggested Citation

  • Heng Cheng & Zebin Xing & Yan Liu, 2023. "The Improved Element-Free Galerkin Method for 3D Steady Convection-Diffusion-Reaction Problems with Variable Coefficients," Mathematics, MDPI, vol. 11(3), pages 1-19, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:770-:d:1056603
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    References listed on IDEAS

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    1. Jing Cheng, 2021. "Mathematical Models and Data Analysis of Residential Land Leasing Behavior of District Governments of Beijing in China," Mathematics, MDPI, vol. 9(18), pages 1-14, September.
    2. Jing Cheng & Xiaowei Luo, 2022. "Analyzing the Land Leasing Behavior of the Government of Beijing, China, via the Multinomial Logit Model," Land, MDPI, vol. 11(3), pages 1-14, March.
    3. Heng Cheng & Guodong Zheng, 2020. "Analyzing 3D Advection-Diffusion Problems by Using the Improved Element-Free Galerkin Method," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-13, August.
    4. 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).
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    Cited by:

    1. Fengbin Liu & Mingmei Zuo & Heng Cheng & Ji Ma, 2023. "Analyzing Three-Dimensional Laplace Equations Using the Dimension Coupling Method," Mathematics, MDPI, vol. 11(17), pages 1-20, August.

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