An improved stabilized element-free Galerkin method for solving steady Stokes flow problems

Combining the dimensional splitting moving least squares (DSMLS) approximation and the variational weak form, this paper developed an improved stabilized element-free Galerkin (ISEFG) method for Stokes problems. In the ISEFG method, the DSMLS approximation is adopted to construct the shape function, and the stabilization factor is established based on the solution space of velocity and pressure. The Galerkin weak form and integral coordinate transformation are taken to achieve the final discrete equations of the problems. Following the ideas of the dimensional splitting method, the DSMLS method approximates the functions from the direction of dimension splitting and the dimension-splitting subdivision surfaces. Then the ISEFG method can reduce the dimensionality and complexity of matrix operations in solving the shape function, thereby improving the efficiency and accuracy. This paper introduces several numerical examples to demonstrate the effectiveness of the stabilized meshless method. The numerical examples show that the ISEFG method based on the DSMLS approximation can find stable solutions of the velocities and pressure without physical oscillation. The method presented in this paper offers higher accuracy and consumes less CPU time than the EFG method based on the MLS approximation.