The Generalized Galerkin’s Equations of the Finite Element, the Boundary Variational Equations and the Boundary Integral Equations

Based on [1], we have further applied the variational principle of the variable boundary to investigate the discretization analysis of the solid system and derived the generalized Ga-lerkin's equations of the finite element, the boundary variational equations and the boundary integral equations.These e-quations indicate that the unknown functions of the solid system must satisfy the conditions in the element S_a or on theboundaries Γ_a.These equations are applied to establishing the discretization equations in order to obtain the numerical solution of the unknown functions. At a time these equations can be used as the basis for the simplified calculation in various corresponding cases.In this paper, the results of boundary integral equations show that the calculation Γ_a of integration is not accurate along the surface of interior element S_a by J-integral suggested by Rice [2].