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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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    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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