AN OUTLINE OF ADAPTIVE WAVELET GALERKIN METHODS FOR TIKHONOV REGULARIZATION OF INVERSE PARABOLIC PROBLEMS

2003 ◽  
Author(s):  
STEPHAN DAHLKE ◽  
PETER MAAß
Keyword(s):  
Tikhonov Regularization ◽  
Parabolic Problems ◽  
Galerkin Methods ◽  
Adaptive Wavelet

scholarly journals An efficient solver for space–time isogeometric Galerkin methods for parabolic problems

2020 ◽  
Vol 80 (11) ◽  
pp. 2586-2603
Author(s):  
Gabriele Loli ◽  
Monica Montardini ◽  
Giancarlo Sangalli ◽  
Mattia Tani
Keyword(s):  
Space Time ◽  
Parabolic Problems ◽  
Galerkin Methods ◽  
Efficient Solver

scholarly journals Adaptive Wavelet Galerkin Methods for Linear Inverse Problems

2004 ◽  
Vol 42 (4) ◽  
pp. 1479-1501 ◽  
Author(s):  
Albert Cohen ◽  
Marc Hoffmann ◽  
Markus Reiss
Keyword(s):  
Inverse Problems ◽  
Galerkin Methods ◽  
Adaptive Wavelet ◽  
Linear Inverse Problems

scholarly journals A modified Tikhonov regularization method for a class of inverse parabolic problems

2020 ◽  
Vol 28 (1) ◽  
pp. 181-204
Author(s):  
Nabil Saouli ◽  
Fairouz Zouyed
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Tikhonov Regularization ◽  
Regularization Method ◽  
Parabolic Problem ◽  
Tikhonov Regularization Method ◽  
Parabolic Problems ◽  
Initial Condition ◽  
Ill Posed ◽  
Convergence Estimates

AbstractThis paper deals with the problem of determining an unknown source and an unknown initial condition in a abstract final value parabolic problem. This problem is ill-posed in the sense that the solutions do not depend continuously on the data. To solve the considered problem a modified Tikhonov regularization method is proposed. Using this method regularized solutions are constructed and under boundary conditions assumptions, convergence estimates between the exact solutions and their regularized approximations are obtained. Moreover numerical results are presented to illustrate the accuracy and efficiency of the proposed method.

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