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A coupled complex boundary expanding compacts method for inverse source problems
Örebro University, School of Science and Technology. Faculty of Mathematics, Chemnitz University of Technology, Chemnitz, Germany . (Mathematics)ORCID iD: 0000-0003-4023-6352
Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, P. R. China .
Örebro University, School of Science and Technology.ORCID iD: 0000-0003-0332-2315
Department of Mathematics, Zhejiang University, Hangzhou, P. R. China.
2019 (English)In: Journal of Inverse and Ill-Posed Problems, ISSN 0928-0219, E-ISSN 1569-3945, Vol. 27, no 1, p. 67-86Article in journal (Refereed) Published
Abstract [en]

In this paper, we consider an inverse source problem for elliptic partial differential equations with both Dirichlet and Neumann boundary conditions. The unknown source term is to be determined by additional boundary data. This problem is ill-posed since the dimensionality of the boundary is lower than the dimensionality of the inner domain. To overcome the ill-posed nature, using the a priori information (sourcewise representation), and based on the coupled complex boundary method, we propose a coupled complex boundary expanding compacts method (CCBECM). A finite element method is used for the discretization of CCBECM. The regularization properties of CCBECM for both the continuous and discrete versions are proved. Moreover, an a posteriori error estimate of the obtained finite element approximate solution is given and calculated by a projected gradient algorithm. Finally, numerical results show that the proposed method is stable and effective.

Place, publisher, year, edition, pages
Walter de Gruyter, 2019. Vol. 27, no 1, p. 67-86
Keywords [en]
Inverse source problem, expanding compacts method, finite element method, error estimation
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:oru:diva-68829DOI: 10.1515/jiip-2017-0002ISI: 000457195600006Scopus ID: 2-s2.0-85053166222OAI: oai:DiVA.org:oru-68829DiVA, id: diva2:1247127
Funder
Knowledge Foundation, 20170059
Note

Funding Agencies:

Alexander von Humboldt foundation  

Natural Science Foundation of China  11571311  11401304 

Fundamental Research Funds for the Central Universities  NS2018047 

Available from: 2018-09-11 Created: 2018-09-11 Last updated: 2019-02-13Bibliographically approved

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Zhang, YeGulliksson, Mårten

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