On a two-level element-free Galerkin method for incompressible fluid flow

In this paper, a new element-free Galerkin method called the two-level element-free Galerkin method is presented for incompressible fluid flow. This method consists of two parts: One at the global level and the other at the local level. The new method is based on the Hughes' variational multiscale formulation, and arises from a decomposition of the unknown variables into coarse/resolved scale and fine/unresolved scale. In order to find the unresolved part of the solution, the momentum equation is used to define the unresolved governing equation on the local level. Finally the application of the proposed method to incompressible fluid flow is displayed. Numerical solutions obtained from the two-level element-free Galerkin method are present for three benchmark problems, and the results indicate that the proposed method is a robust and accurate method. This is due to the addition of the unresolved scale which adds stability to the discrete problem when equal order basis is used for pressure and velocity.