On two-coefficient identification in elliptic variational inequalities

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.

Keywords:

• Variable parameter identification
• ellipticity parameter
• Helmholtz parameter
• Robin parameter
• trilinear form
• vector approximation
• Mosco set convergence
• Galerkin method

Acknowledgements

The author wants to thank the anonymous referees for their insightful comments.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

Dedicated to Prof. Johannes Jahn on the occasion of his 65th birthday in remembrance of our joint time at Darmstadt.