Trapezoidal Nested Encryption Finite Element Method And The Analysis Of Convergence

The finite element method is an important method of solving all kinds of complex mathe-matics and physical problems. In the development of digital information means today, the finite element method has become an important tool for scientific research and engineering computing indispensable. It is the mature and effective method of numerical solving differential equations. In this paper, we use the nested refinement finite element adaptive technology to study the trape-zoidal nested refinement finite element method and the basic properties. The trapezoidal nested refinement finite element method for the second order self-adjoint elliptic boundary value prob-lems and convergence analysis results are given. Then we introduce the finite element method with Q1truncations, and the conclusions of convergence analysis are given. Furthermore, a numerical example is given to illustrate the theoretical analysis results which are feasible and effective.Structural framework of this paper are as follows:In chapter Ⅰ, the introduction describes the history of the development and research status of finite element method and adaptive finite element, and gives the basic knowledge to use in this paper.In chapter Ⅱ, some basic properties of the trapezoidal nested refinement finite element are discussed and studied, and the trapezoidal nested refinement finite element method for the sec-ond order self-adjoint elliptic boundary value problems and the results of convergence analysis are also given.In chapter Ⅲ, the trapezoidal nested refinement finite element method with Qi truncations for the boundary value problems of Poisson equation is introduced, and the convergent results are given.In chapter Ⅳ, a numerical example is given to illustrate the theoretical analysis results.