The Finite Volume Element Method Of A Class Of Parameter Identification Problems

In this paper,we put forward to use the finite volume element method for the numericalsolution method.The question is based on the inverse problem, which with additionalconditions of parabolic partial differential equations of the parameter identification problem.The finite volume element method, also known as finite difference method, was proposed byProfessor Li Ronghua firstly. This method is simple, accurate, and keeps the physicalconservation.In the paper, the equations(?)are studied on homogeneous and non-homogeneous form. Firstly, we translate the former tothe linear parabolic equations, then use the finite volume element to partition in space andbackward difference, forward difference in time. We get some unknown parameters andcontrol parameters of numerical; at the same time we estimate the error and proof it. Theexample is the best proof to its convergence. Secondly, to the latter,we do the sametransformation and discrete, give its unknown parameters and control parameters of thenumerical schemes and error estimation, and through numerical examples verify its highdegree of accuracy. Finally, to the latte, we have another method to solove,that is the directlyfinite volume element triangulation, by iterative given its numerical schemes. In each chapterfor additional points are discussed at the mesh node and between two nodes.