Standard Galerkin Finite Element Method Considering Compensation Stiffness in Fluid Mechanics

Abstract:

The wave problems of the finite element solution of one dimensional steady state convection diffusion equation was analyzed. It is indicated that the continuity improvement of the shape function between elements is an effective method to decrease the amplitude of wave. Based on the standard Galerkin (SG) finite element method, the compensation term considering the elastic stiffness was introduced by adding an “unbalanced force” to the nodes between elements, to form a complemental standard Galerkin (CSG) finite element equation. The expressions of compensation stiffness of linear Lagrange based interpolation (LLBI) function and exponential function based interpolation (EFBI) function were discussed. The results obtained by CSG and SG were compared with those of the analytical solution. It shows that the continuity of the shape function is improved and the amplitude of wave is decreased when the compensation term is introduced into the SG finite element. Compared with the SG finite element using LLBI, the CSG finite element using EFBI is more effective to control the wave phenomenon since it has a better continuity both inside the element and between two elements.