On Linear Finite Elements for Simultaneously Recovering Source Location and Intensity

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.