Identification problems with given material interfaces

0482339 - ÚGN 2018 RIV NL eng J - Journal Article
Haslinger, Jaroslav - Blaheta, Radim - Hrtus, Rostislav
Identification problems with given material interfaces.
Journal of Computational and Applied Mathematics. Roč. 310, January 2017 (2017), s. 129-142. ISSN 0377-0427. E-ISSN 1879-1778
R&D Projects: GA MŠMT ED1.1.00/02.0070; GA MŠMT LQ1602
Institutional support: RVO:68145535
Keywords : identification of conductivity coefficients * control of systems by coefficients of PDE * algebraic sensitivity analysis * scalarization technique * pumping test
OECD category: Applied mathematics
Impact factor: 1.632, year: 2017
http://www.sciencedirect.com/science/article/pii/S0377042716302953

This paper is devoted to the identification of coefficients in scalar elliptic partial differential
equations using an optimal control approach. The coefficients usually can be interpreted
as material characteristics and play the role of the control variable. The paper focuses on
processes in domains which can be split into a finite number of materially homogeneous
subdomains, i.e. the coefficients to be identified are piecewise constant on them. In
addition, we assume that the material interfaces are a priori known.Weprove the existence
of at least one solution of the optimal control problem for a large class of cost functionals
and show that solutions can be obtained as limits of solutions to the problems which
are governed by finite element discretizations of the state equations. Further, the unified
algebraic sensitivity analysis of the first and the second order for several least squares type
cost functions is investigated. Finally, a model problem of the identification of coefficients
characterizing hydraulic conductivity by pumping tests in groundwater flow modeling is
numerically solved using the sequential approach and the scalarization technique.
Permanent Link: http://hdl.handle.net/11104/0277752