A hybrid generalized interpolated element-free Galerkin method for Stokes problems

Abstract

By coupling the ideas of dimension splitting method (DSM) and the generalized element-free Galerkin (GEFG) method, a hybrid generalized interpolated element-free Galerkin (HGIEFG) method is developed for Stokes problems. In the HGIEFG method, the two-dimensional problem splits into a battery of one-dimensional problems by the DSM. Combining the improved interpolating moving least-squares (IIMLS) method, the GEFG method is applied to obtain the discrete equations of the one-dimensional problems on the splitting plane. And then final discretized equations of the whole Stokes problems are assembled by the IIMLS method. Compared with the EFG method, the HGIEFG method can obtain non-oscillating solutions of pressure for Stokes problems. Compared with the variational multiscale element-free Galerkin (VMEFG) method, the stabilization technique in HGIEFG method is only related to nodes but not to integral grids. Compared with the EFG, VMEFG and GEFG methods, the HGIEFG method has higher computational efficiency. Numerical examples show that the HGIEFG method can obtain non-oscillating solutions of pressure and velocity, and has higher efficiency and accuracy for Stokes problems.