Please use this identifier to cite or link to this item: https://dspace.ctu.edu.vn/jspui/handle/123456789/100892
Title: Energy space approaches to the cauchy problem for Poisson's equation
Authors: Phan, Xuan Thanh
Steinbach, Olaf
Keywords: Cauchy problem
Variational method
Energy space
Boundary element method
Error estimate
Issue Date: 2020
Series/Report no.: Acta mathematica Vietnamica journal;Vol.45, No.03 .- P.693-707
Abstract: Variational methods coupled with Tikhonov's regularization for solving the cauchy problem for Poisson's equation are suggested and studied. The novel idea is to use the Tikhonov regularization term in H½ norm rather than in L₂ norm. The penalty term is evaluated by some appropriate boundary integral operators. The optimality condition in the form of boundary integral equations is derived and then discretized by the Galerkin boundary element method. The error estimates for the discretized problems are proved for noisy data. Some numerical examples and comparisons with the L₂ setting are presented for showing the efficiency of our approaches.
URI: https://dspace.ctu.edu.vn/jspui/handle/123456789/100892
ISSN: 0251-4184
Appears in Collections:Acta Mathematica Vietnamica 

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