Abstract
We consider an obstacle model mathematically described by means of a boundary value problem governed by PDE. Three possible variational formulations are highlighted. The first one is a variational inequality of the first kind and the other two are mixed variational formulations with Lagrange multipliers in dual spaces. After we discuss the solvability of the three variational formulations under consideration we focus on the relationship between them. Subsequently, we address the recovery of the formulation in terms of PDE starting from the mixed variational formulations.
Publisher
Academia Oamenilor de Stiinta din Romania
Reference29 articles.
1. [1] R.A. Adams. Sobolev spaces, Academic Press, 1975.
2. [2] H. Brezis. Functional Analysis, Sobolev Spaces and Partial Differential Equations, Spriger, 2010.
3. [3] D. Boffi, F. Brezzi, M. Fortin. Mixed Finite Element Methods and Applications, Springer Series in Computational Mathematics 44, SpringerVerlag Berlin Heidelberg 2013.
4. [4] F. Bonnans, D. Tiba. Pontryagin's principle in the control of elliptic variational inequalities, Appl. Math. Optim. 23(1):299-312, 1991.
5. [5] D. Braess. Finite elements. Theory, fast solvers, and applications in solid mechanics, Second edition, Cambridge University Press 2001.