American Institute of Mathematical Sciences

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November  2010, 14(4): 1641-1670. doi: 10.3934/dcdsb.2010.14.1641

Error estimates of finite element methods for parameter identifications in elliptic and parabolic systems

Lijuan Wang 1, and  Jun Zou 2,

1. 

Department of Mathematics, Wuhan University, Wuhan 430072, China
2. 

Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong

Received  November 2009 Revised  April 2010 Published  August 2010

This work is concerned with the finite element solutions for parameter identifications in second order elliptic and parabolic systems. The $L^2$- and energy-norm error estimates of the finite element solutions are established in terms of the mesh size, time step size, regularization parameter and noise level.
Keywords: error estimates., parameter identification, regularization parameter, Tikhonov regularization, finite element method, noise level.
Mathematics Subject Classification: Primary: 35R30, 65M30; Secondary: 65N1.
Citation: Lijuan Wang, Jun Zou. Error estimates of finite element methods for parameter identifications in elliptic and parabolic systems. Discrete & Continuous Dynamical Systems - B, 2010, 14 (4) : 1641-1670. doi: 10.3934/dcdsb.2010.14.1641
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