In this paper we consider Galerkin finite element discretizations of semilinear elliptic differential inclusions that satisfy a relaxed one-sided Lipschitz condition. The properties of the set-valued Nemytskii operators are discussed, and it is shown that the solution sets of both, the continuous and the discrete system, are nonempty, closed, bounded, and connected sets in H1-norm. Moreover, the solution sets of the Galerkin inclusion converge with respect to the Hausdorff distance measured in Lp-spaces.
|Number of pages||18|
|Journal||Discrete and Continuous Dynamical Systems - Series B|
|Publication status||Published - Mar 2013|
- Elliptic partial differential inclusions
- Finite element methods
- Set-valued numerical analysis
- Uncertainty quantification