Analysis of the complex moving least squares approximation and the associated element-free Galerkin method

作者：Li, Xiaolin^*; Li, Shuling

来源：Applied Mathematical Modelling, 2017, 47: 45-62.

DOI：10.1016/j.apm.2017.03.019

• Meshless
• Complex variable
• Moving least squares approximation
• Element-free Galerkin method
• Stability
• Error estimate

The complex moving least squares approximation is an efficient method to construct approximation functions in meshless methods. This paper begins by analyzing properties, stability and error of the approximation. To overcome the inherent instability, a stabilized approximation is also developed and analyzed. The complex element-free Galerkin method is a meshless method combined with the use of the complex moving least squares approximation. Application of the complex element-free Galerkin method to linear and nonlinear time-dependent problems is then given. Error estimates of the complex element-free Galerkin method are derived theoretically. Numerical examples involving function fitting and solitons are finally provided to show the accuracy and efficiency of the proposed methods.

• 出版日期2017-7
• 单位重庆师范大学