TY - JOUR
T1 - On Linear Finite Elements for Simultaneously Recovering Source Location and Intensity
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 - <p style="text-align: justify;">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.</p>