Simultaneous identification of convection velocity and source strength in a convection–diffusion equation. Issue 12 (9th September 2020)

• Record Type: Journal Article
• Authors: Cheng, Ting; Hu, Junjun; Jiang, Daijun
• Is Part Of: Applicable analysis. Volume 99:Issue 12(2020)
• Page Start: 2170
• Page End: 2189
• Publication Date: 2020-09-09
• Subjects: J. Zou; Inverse problems -- simultaneous identification -- time-dependent convection–diffusion system -- finite element method; 41A25 -- 65M32; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1555326
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : In this work we are concerned with the analysis on a simultaneous finite element reconstruction of the convection velocity and source strength in a time-dependent convection–diffusion equation. The ill-posed problem is formulated into an output least-squares nonlinear minimization by an appropriately selected Tikhonov regularization. The regularizing effect and mathematical properties of the regularized system are justified and demonstrated. The nonlinear optimization problem is approximated by a fully discrete finite element method, whose convergence is rigorously established.