Meshless Galerkin analysis of the generalized Stokes problem

Abstract

This paper proposes and analyzes a stabilized element-free Galerkin (EFG) method for meshless Galerkin analysis of the generalized Stokes problem. The Nitsche-type weak form of the generalized Stokes problem is derived by adopting Nitsche's technique to deal with the lack of interpolation property of meshless shape functions. By introducing the residual-based stabilization technique to establish a stabilized Nitsche-type EFG weak form, the proposed stabilized EFG method not only allows equal-order approximation spaces for velocity and pressure, but also applies to the generalized Stokes problem with small viscosity and large reaction coefficient. Both the inf-sup stability and the error estimation of the stabilized EFG method are analyzed theoretically. Some numerical results are provided to demonstrate the efficiency of the method.