Simultaneous identification of convection velocity and source strength in a convection–diffusion equation

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.

COMMUNICATED BY:

• J. Zou

Keywords:

• Inverse problems
• simultaneous identification
• time-dependent convection–diffusion system
• finite element method

2010 Mathematics Subject Classifications:

• 41A25
• 65M32

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work of this author was financially supported by National Natural Science Foundation of China [Nos. 11871240, 11771170, 11401241 and 11571265] and NSFC-RGC [China-Hong Kong, No. 11661161017].