On two-coefficient identification in elliptic variational inequalities. (3rd July 2018)

• Record Type: Journal Article
• Authors: Gwinner, Joachim
• Is Part Of: Optimization. Volume 67:Number 7(2018)
• Page Start: 1017
• Page End: 1030
• Publication Date: 2018-07-03
• Subjects: Variable parameter identification -- ellipticity parameter -- Helmholtz parameter -- Robin parameter -- trilinear form -- vector approximation -- Mosco set convergence -- Galerkin method; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1446955
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: This paper is concerned with elliptic variational inequalities that depend on two parameters. First, we investigate the dependence of the solution of the forward problem on these parameters and prove a Lipschitz estimate. Then, we study the inverse problem of identification of these two parameters and formulate two optimization approaches to this parameter identification problem. We extend the output least-squares approach, provide an existence result and establish a convergence result for finite-dimensional approximation. Further, we investigate the modified output least-squares approach which is based on energy functionals. This latter approach can be related to vector approximation.