The finite element method is a mathematical principle of the Pan - Han variational principle or the right equation cushion with orthogonal function Principle. For a given set of hydrodynamic certain issues, if we can find the energy functionals they can establish a functional energy minimization of the fractional change. And the other unable to obtain energy functional fluid, it is usually from the corresponding differential equations, According to equation cushion orthogonal function with the right of principle, establish weighted residual expression. This variation is the expression or the weighted residual integral expression, Hydrodynamics is real physical interval for the finishing of a mathematical description of the hydrodynamics of a mathematical model, and differential equations have the same significance. Through this integral expression for solving the traditional method of Ritz_Calerkin methods. And FEM side rules of the emerging high-speed electronic computers, In Ritz_Calerkin methods developed on the basis of numerical calculation method; In essence can be said to be a rule of the special type of Ritz_Calerkin methods.
Finite Element Methods for Discrete the main ideas of "block approach." Is the solution of regional subdivided into a finite number of complementary overlapping sub-regional, sub-regional as "modules"; in each of the modules in vivo, we have selected several months as a suitable point for the interpolation function, called "nodes." The unit will function for a rule-based function of the linear approximation to replace the portfolio, The coefficient of linear combination is for Function nodes in the function. Thus, the integral unit will be available
FEM equation, after cumulative available finite element equations. By solving finite element equations, Get all
nodes on the function.
For the finite element method, the basic ideas and problem-solving steps can be summarized as
(1)Integral equation. according to the variational principle, or the right equation cushion with orthogonal function of principle, and the establishment of differential equations equivalent to the initial boundary value problem integral expression, which is the finite element method starting point.
(2)regional unit subdivision.  according to the shape of the region to solve practical problems and the physical characteristics, regional subdivision for a number of interlinked, not overlapping modules. Regional Unit Division is using the finite element method in the early stage of preparations, some of the workload is bigger, In addition to the unit of calculation and node numbering and identification of the inter-relationship between, would also like to express the position of node coordinates, There is also the need to set out the nature and the natural boundary of the boundary nodes serial number and the corresponding boundary value.
(3)Identify basic function modules. modules and the number of nodes on the approximate solution accuracy requirements, choose to meet certain conditions of the interpolation function interpolation function as a base unit. Finite element method is the basic function of the selected modules, the modules with the rules of geometry. When selecting basic function may follow certain rules.
(4)Analysis modules . all modules function for the base unit with a linear combination of function expressions approximation; Approximate function then incorporated into the integral equation, as well as modules for regional integration, available containing undetermined coefficient (that is, each node module parameter values) of the algebraic equations, known as FEM equation.
(5)Overall Synthesis : Subject to the FEM equation, the region will all FEM equation by certain rules for accumulation, formation of the overall finite element equations.
(6)Deal with the boundary conditions : general boundary conditions in three forms, namely essential boundary conditions (Dirichlet boundary conditions. natural boundary conditions (Riemann boundary conditions), the mixed boundary conditions (Cauchy boundary conditions). natural boundary conditions, In general integral expression can be automatically met. For boundary conditions and the nature of mixed boundary conditions, They have certain rules of the overall finite element equations that meet.
(7)Solveing finite element equation : According to the boundary conditions that the overall finite element equations. is to be determined with all the unknowns closed equations with the appropriate numerical calculation method to solve, each node can be obtained the function.

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