Coupling Methods Based On Natural Boundary Reduction For Two Types Of Problems

This thesisi is mainly based on the coupling method of natural boundary element and finite element to study the Poisson equation and quasi linear problems in concave corner regions.The specific content is as follows:Chapter 1 provides a detailed overview of the progress in coupling natural boundary element and finite element methods in recent years,as well as relevant mathematical theoretical knowledge.In Chapter 2,based on the basic principle of natural boundary reduction,a coupling method between curved edge finite element and natural boundary element is presented.The coupling method was used to solve the boundary value problem of the Poisson equation in a concave corner region,and the error estimation and convergence of the approximate solution were obtained.Finally,numerical examples are used to demonstrate the feasibility and effectiveness of the method.In chapter 3,the coupling method of natural boundary element and finite element is used to solve the coupled nonlinear problem,that is,an artificial boundary circle is added,and the natural integral equation on the circle is obtained by using the natural edge reduction principle,which proves the convergence of the coupling method.Finally,the corresponding numerical examples are given to prove the feasibility and effectiveness of the method.