A Posteriori Regularization Parameter Choice Rule for Truncation Method for Identifying the Unknown Source of the Poisson Equation | Zendy

Xiaoxiao Li | Zendy; Dun-Gang Li | Zendy

Open Access

A Posteriori Regularization Parameter Choice Rule for Truncation Method for Identifying the Unknown Source of the Poisson Equation

Author(s) -

Xiaoxiao Li,

Dun-Gang Li

Publication year - 2013

Publication title -

international journal of partial differential equations

Language(s) - English

Resource type - Journals

eISSN - 2356-7082

pISSN - 2314-6524

DOI - 10.1155/2013/590737

Subject(s) - regularization (linguistics) , a priori and a posteriori , truncation (statistics) , mathematics , mathematical optimization , poisson distribution , stability (learning theory) , poisson's equation , computer science , statistics , mathematical analysis , artificial intelligence , machine learning , philosophy , epistemology

We consider the problem of determining an unknown source which depends only on one variable in two-dimensional Poisson equation. We prove a conditional stability for this problem. Moreover, we propose a truncation regularization method combined with an a posteriori regularization parameter choice rule to deal with this problem and give the corresponding convergence estimate. Numerical results are presented to illustrate the accuracy and efficiency of this method

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