Abstract
In this study, a variational multiscale interpolating element-free Galerkin (VMIEFG) method is developed for numerical analysis of Darcy flow. In the VMIEFG method, the improved interpolating moving least squares method is used to construct shape functions with interpolating properties. Then, the no-penetration boundary condition of Darcy flow can be satisfied exactly. Meanwhile, the utilization of Hughes’ variational multiscale formulation eliminates the numerical oscillation in the standard element-free Galerkin method. Thus, the VMIEFG method permits equal-order basis for both the velocity and pressure, and the restraint of the Babuška-Brezzi condition is violated completely. Numerical results demonstrate that the present VMIEFG method has high accuracy and stability for solving Darcy flow.
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