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Volume 10, Issue 3
On Linear Finite Elements for Simultaneously Recovering Source Location and Intensity

X. Deng, Y. Zhao & J. Zou

Int. J. Numer. Anal. Mod., 10 (2013), pp. 588-602.

Published online: 2013-10

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  • Abstract

Linear elements are least expensive finite elements for simultaneously recovering the source location and intensity in a general convection-diffusion process. However, the derivatives of the least-squares objective functional with Tikhonov regularizations are not well-defined when linear finite elements are used. In this work we provide a systematic formulation of the numerical inversion using linear finite elements and propose some effective techniques to overcome the undefinedness that may occur in inversion process. We show that linear finite elements can be made very robust and efficient in simultaneously recovering the source location and intensity. Numerical results are presented to validate the robustness and effectiveness of the proposed algorithm.

  • Keywords

source location, source intensity, convection-diffusion and linear finite elements.

  • AMS Subject Headings

35R35, 49J40, 60G40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-10-588, author = {X. Deng, Y. Zhao and J. Zou}, title = {On Linear Finite Elements for Simultaneously Recovering Source Location and Intensity}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2013}, volume = {10}, number = {3}, pages = {588--602}, abstract = {

Linear elements are least expensive finite elements for simultaneously recovering the source location and intensity in a general convection-diffusion process. However, the derivatives of the least-squares objective functional with Tikhonov regularizations are not well-defined when linear finite elements are used. In this work we provide a systematic formulation of the numerical inversion using linear finite elements and propose some effective techniques to overcome the undefinedness that may occur in inversion process. We show that linear finite elements can be made very robust and efficient in simultaneously recovering the source location and intensity. Numerical results are presented to validate the robustness and effectiveness of the proposed algorithm.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/584.html} }
TY - JOUR T1 - On Linear Finite Elements for Simultaneously Recovering Source Location and Intensity AU - X. Deng, Y. Zhao & J. Zou JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 588 EP - 602 PY - 2013 DA - 2013/10 SN - 10 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/584.html KW - source location, source intensity, convection-diffusion and linear finite elements. AB -

Linear elements are least expensive finite elements for simultaneously recovering the source location and intensity in a general convection-diffusion process. However, the derivatives of the least-squares objective functional with Tikhonov regularizations are not well-defined when linear finite elements are used. In this work we provide a systematic formulation of the numerical inversion using linear finite elements and propose some effective techniques to overcome the undefinedness that may occur in inversion process. We show that linear finite elements can be made very robust and efficient in simultaneously recovering the source location and intensity. Numerical results are presented to validate the robustness and effectiveness of the proposed algorithm.

X. Deng, Y. Zhao and J. Zou. (2013). On Linear Finite Elements for Simultaneously Recovering Source Location and Intensity. International Journal of Numerical Analysis and Modeling. 10 (3). 588-602. doi:
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