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Analyzing 3D Advection-Diffusion Problems by Using the Improved Element-Free Galerkin Method

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  • Heng Cheng
  • Guodong Zheng

Abstract

In this paper, the improved element-free Galerkin (IEFG) method is used for solving 3D advection-diffusion problems. The improved moving least-squares (IMLS) approximation is used to form the trial function, the penalty method is applied to introduce the essential boundary conditions, the Galerkin weak form and the difference method are used to obtain the final discretized equations, and then the formulae of the IEFG method for 3D advection-diffusion problems are presented. The error and the convergence are analyzed by numerical examples, and the numerical results show that the IEFG method not only has a higher computational speed but also can avoid singular matrix of the element-free Galerkin (EFG) method.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnlmpe:4317538
    DOI: 10.1155/2020/4317538
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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.
    2. 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.

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