In this thesis, a finite element method for two-dimensional, steady-state viscous incompressible flow using nodeless variables is presented. The corresponding finite element equations are derived from the set of partial differential equations which satisfy the law of conservation of mass and conservation of momentums. Non-linearity is treated with Newton-Raphson iterative method. Moreover, an adaptive meshing technique is implemented to increase the solution accuracy. By using large elements where the solution gradient is low and using smaller elements where the solution gradient is high, time and size of memory required in computation are decreased. This technique also makes the computation of large-complex problems possible. To verify the finite element program, it is used to solve several flow problems of which exact solutions, experimental results, or numerical results are available. The adaptive meshing technique is applied to improve the solution accuracy of more complex problems. The results assure the efficiency of the finite element method proposed in this thesis.
