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有限差分方法、有限元方法、有限体积方法(国外英文资料)
有限差分方法、有限元方法、有限体积方法(国外英文资料)
Finite difference method, finite element method, finite volume method
I. three profiles
The finite difference method (Finite, Difference, Methods) is the earliest method used in numerical simulation of partial differential equations. It is still widely used today. The method includes area partitioning and difference quotient instead of derivative two processes. Specifically, firstly, the solution region is divided into differential meshes, and the finite grid nodes are used instead of the continuous solution regions. Secondly, by using Taylor series expansion method will use derivative function values at the grid points difference in partial differential equations instead of discrete, and to establish the grid values for the algebraic equations of the. This method is a kind of approximate numerical method that directly converts differential problems into algebraic problems. The mathematical concept is intuitive and the expression is simple. It is an earlier and more mature Numerical method. After the difference quotient instead of derivative format format for finite difference format, from precision to consider, one order scheme and two order scheme and high order schemes. The central form and upwind scheme are considered in terms of the spatial discretization of the difference. For transient equations, we consider the discretization of time direction, such as explicit schemes, implicit schemes, alternating explicit schemes, etc.. At present, the common difference schemes are mainly a combination of several formats, and different combinations form different difference schemes. The difference method is mainly applicable to the structured mesh, and the grid step size is usually determined by the model and the Courant stability condition.
The basis of the finite element method (Finite, Element, Methods) is variational principle and piecewise polynomial interpolation. The construction of the method consists of the following three steps. Firs
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