Type of Document Dissertation Author Ramirez, Edgardo II Author's Email Address email@example.com URN etd-0698-13015 Title Finite element methods for parameter identification problem of linear and nonlinear steady-state diffusion equations Degree PhD Department Mathematics Advisory Committee
Advisor Name Title Burns, John A. Rogers, Robert C. Russell, David L. Sun, Shu-Ming Lin, Tao Committee Chair Keywords
- Parameter identification
- Elliptic PDEs
- Finite Element Methods
- Optimization Algorithms
Date of Defense 1997-12-17 Availability unrestricted AbstractWe 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
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.
will be given to show features of this numerical method.
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