有限元分析离散方法（Discrete method of finite element analysis）.doc

有限元分析离散方法（Discrete method of finite element analysis） Discretization method: finite difference method, finite element method, finite volume method Regional discretization, In essence, a finite set of discrete points is used to replace the original continuous space. The implementation process is to divide the calculated region into many overlapping sub regions, determine the location of each sub region and the control volume represented by the node. Node: the geometric position of unknown physical quantities to be solved; control volume: the smallest geometric unit of applied control equations or conservation laws. Nodes are generally regarded as representatives of control volume. The control volume and the subregion are not always coincident. At the beginning of the region discretization process, a small area divided by a series of linear or curve clusters corresponding to the coordinate axis is called a subregion. Grid is the basis of discretization, and grid node is the storage location of discrete physical quantities. As we all know, the commonly used discretization methods are: finite difference method, finite element method, finite volume method. The 1. finite difference method is the most classical method in numerical solution. It is the domain is divided into difference grid, solving the continuous domain with a finite number of grid nodes instead, then the partial differential equation (equations) of the derivative with difference quotient instead, derived with discrete point finite difference equations. This method is developed earlier and more mature, and is used to solve hyperbolic and parabolic problems. It is not convenient to use finite element method or finite volume method to solve complex boundary conditions, especially elliptic problems. 2. the finite element method is a small element of many continuous solution domain is arbitrarily divided into proper shape, and the piecewise interpolation function in each unit, and then according to the extremum