The Finite Volume Element Method for a Class of Parameter Identification Problem with Overspecified-Data

For the parameter identification problem of parabolic partial differential equation with over specified-data, this paper put forwards the method of using the finite volume element method. We provide the numerical scheme of the unknown function and control parameters by using the finite volume element to approximate the spatial derivative of the dependent variable and a simple backward difference to approximate the temporal derivative of the dependent variable. Then the results of the numerical experiment are presented and are compared with the exact solution to confirm the good accuracy of the presented scheme.

[1]  Qian Li,et al.  Generalized difference method , 1997 .

[2]  Zhiqiang Cai,et al.  The finite volume element method for diffusion equations on general triangulations , 1991 .

[3]  Mehdi Dehghan,et al.  Method of lines solutions of the parabolic inverse problem with an overspecification at a point , 2009, Numerical Algorithms.

[4]  Mehdi Dehghan,et al.  The radial basis functions method for identifying an unknown parameter in a parabolic equation with overspecified data , 2007 .

[5]  Zhiqiang Cai,et al.  On the finite volume element method , 1990 .

[6]  Ronghua Li.  Generalized Difference Methods for Differential Equations: Numerical Analysis of Finite Volume Methods , 2000 .

[7]  John R. Cannon,et al.  A class of non-linear non-classical parabolic equations , 1989 .

[8]  Yanping Lin,et al.  Determination of parameter p(t) in Holder classes for some semilinear parabolic equations , 1988 .

[9]  Zhiqiang Cai,et al.  On the accuracy of the finite volume element method for diffusion equations on composite grids , 1990 .

[10]  Mehdi Dehghan,et al.  Parameter determination in a partial differential equation from the overspecified data , 2005, Math. Comput. Model..

[11]  John R. Cannon,et al.  Numerical solutions of some parabolic inverse problems , 1990 .

[12]  Yanping Lin,et al.  An inverse problem of finding a parameter in a semi-linear heat equation , 1990 .

[13]  Mehdi Dehghan.  Identifying a control function in two-dimensional parabolic inverse problems , 2003, Appl. Math. Comput..

[14]  Identifying the temperature distribution in a parabolic equation with overspecified data using a multiquadric quasi-interpolation method , 2010 .