A variational multiscale interpolating element-free Galerkin method for convection-diffusion and Stokes problems

作者：Zhang, Tao; Li, Xiaolin^*

来源：Engineering Analysis with Boundary Elements, 2017, 82: 185-193.

DOI：10.1016/j.enganabound.2017.06.013

• Meshless method
• Interpolating moving least squares method
• Variational multiscale method
• Convection-diffusion problem
• Convection-dominated problem
• Stokes problem

By combining the interpolating moving least squares (IMLS) method with the variational multiscale method, a variational multiscale interpolating element-free Galerkin (VMIEFG) method is presented in this paper for the numerical solutions of convection-diffusion and Stokes problems. In the VMIEFG, the IMLS is used to construct shape functions based on using shifted and scaled polynomial bases. Compared with the variational multiscale element-free Galerkin (VMEFG) method, the VMIEFG method can directly apply the essential boundary conditions. The VMIEFG method is an effective meshless method, especially, for convection-dominated problems. Numerical examples show that the VMIEFG method avoids the oscillation in the element-free Galerkin (EFG) method, and the computational precision of the VMIEFG method is higher than that of the EFG, the VMEFG and the finite element methods.

• 出版日期2017-9
• 单位重庆大学; 重庆师范大学