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

Fengxin Sun, Jufeng Wang, Xiang Kong and Rongjun Cheng
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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

Mathematics, 2021, vol. 9, issue 19, 1-15

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.

Keywords: meshless method; dimension splitting method; dimension splitting generalized interpolating element-free Galerkin method; convection–diffusion–reaction problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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