Title page for ETD etd-0698-13015


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 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
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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