Regularization and Error Estimate for the Poisson Equation with Discrete Data

Nguyen Anh Triet, Nguyen Duc Phuong, Nguyen Van Thinh and Can Nguyen-Huu
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Nguyen Anh Triet: Faculty of Natural Sciences, Thu Dau Mot University, Thu Dau Mot City 820000, Binh Duong Province, Vietnam
Nguyen Duc Phuong: Faculty of Fundamental Science, Industrial University of Ho Chi Minh City, Ho Chi Minh City 700000, Vietnam
Nguyen Van Thinh: Department of Civil and Environmental Engineering, Seoul National University, Seoul 08826, South Korea
Can Nguyen-Huu: Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam

Mathematics, 2019, vol. 7, issue 5, 1-20

Abstract: In this work, we focus on the Cauchy problem for the Poisson equation in the two dimensional domain, where the initial data is disturbed by random noise. In general, the problem is severely ill-posed in the sense of Hadamard, i.e., the solution does not depend continuously on the data. To regularize the instable solution of the problem, we have applied a nonparametric regression associated with the truncation method. Eventually, a numerical example has been carried out, the result shows that our regularization method is converged; and the error has been enhanced once the number of observation points is increased.

Keywords: Poisson problem; Ill-posed problem; discrete data (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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