Meshless analysis of two-dimensional Stokes flows with the Galerkin boundary node method

In this paper, the Galerkin boundary node method (GBNM) is developed for the solution of stationary Stokes problems in two dimensions. The GBNM is a boundary only meshless method that combines a variational form of boundary integral formulations for governing equations with the moving least-squares (MLS) approximations for construction of the trial and test functions. Boundary conditions in this approach are included into the variational form, thus they can be applied directly and easily despite the MLS shape functions lack the property of a delta function. Besides, the GBNM keeps the symmetry and positive definiteness of the variational problems. Convergence analysis results of both the velocity and the pressure are given. Some selected numerical tests are also presented to demonstrate the efficiency of the method.