The 2-d Axial Symmetry Immersed Finite Element Method For The Plasma Numerical Simulation

The research on immersed finite elements is motivated by many real world applications, in which a simulation domain is often formed by several materials separated from each other by curves or surfaces while a mesh independent of interface. The bilinear IFE methods'mesh can be independent of interface. Numerical examples show that these methods based on the bilinear IFE methods have the same optimal convergence rates as those based on the standard bilinear finite element for solutions. So how to apply this method becomes an important work in the world. When we apply the bilinear IFE methods into IFE-PIC methods, we find out that the traditional charge deposit methods have some bad influences on the result of our simulation. So how to solve this problem becomes a hot field in modern research.In this dissertation we discuss bilinear immersed finite elements (IFE) for solving interface problems. The related research works can be categorized into three aspects: (1) the construction of the bilinear immersed finite element methods; (2) numerical methods based on these IFE methods for solving interface problems; and (3) the corresponding error analysis. For applying this method into project, we have programmed some Fortran programs, and tested the programs by using some examples.Next, we would introduce the traditional charge deposit method in different coordinate system, and analysis the faults of the traditional charge deposit method. After the analysis, we bring some new methods such as"WILHELMUS M.RUYTEN","DAVID J. LARSON"and"VERBONCOEUR". We would prove that"DAVID J. LARSON"and"VERBONCOEUR"are equivalent but just some form differences.Finally, by programming Fortran programs, we could contrast the three methods, and deal with the results of the programs for the convenience of our analysis.