The Study On High Accuracy Full-discrete Method And Its Convergence Of A Class Of Parameter Identification Problems

In order to solve the problem of parameter identification for a class of parabolic differential equations with additional conditions,the quadratic finite volume element method is proposed for semi-discretization in space and the quadratic continuous finite element method for complete discretization in time.The numerical solution of unknown function and control parameter stability is derived.In this paper,the problem of parameter identification is studied from special to general.Firstly,the situation of homogeneous boundary of homogeneous equations is studied.The parameter identification problem is transformed into a positive problem without parameters by transformation.Then,the quadratic finite volume element method is proposed for semi-discretization in space and the quadratic continuous finite element method for complete discretization in time.The fully-discrete calculation scheme is derived,and the error analysis of the corresponding format is given.Finally,a numerical example is given to verify the stability and effectiveness of the proposed scheme.Similarly,the homogeneous boundary of non-homogeneous equations and the non-homogeneity of the general case are studied in the same way.The numerical solution of unknown function and control parameter stability is derived,and the error analysis of the corresponding format is given.Finally,each of the two situations is illustrated with a numerical example and their stability and effectiveness of the proposed scheme is fully analyzed and discussed.