Type of Document	Dissertation
Author	Ramirez, Edgardo II
Author's Email Address	ramirez@math.vt.edu
URN	etd-0698-13015
Title	Finite element methods for parameter identification problem of linear and nonlinear steady-state diffusion equations
Degree	Doctor of Philosophy
Department	Mathematics Department
Advisory Committee	Advisor Name Title David Russell John Burns Robert Rogers Shu-Ming Sun Tao Lin chair
Keywords	Parameter identification Elliptic PDEs Finite Element Methods Optimization Algorithms
Date of Defense	1997-12-17
Availability	unrestricted
Abstract We study a parameter identification problem for the steady state diffusion equations. In this thesis, we transform this identification problem into a minimization problem by considering an appropriate cost functional and propose a finite element method for the identification of the parameter for the linear and nonlinear partial differential equation. The cost functional involves the classical output least square term, a term approximating the derivative of the piezometric head u(x), an equation error term plus some regularization terms, which happen to be a norm or a semi-norm of the variables in the cost functional in an appropriate Sobolev space. The existence and uniqueness of the minimizer for the cost functional is proved. Error estimates in a weighted H-1-norm, L2-norm and L1-norm for the numerical solution are derived. Numerical examples will be given to show features of this numerical method.
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