Abstract
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.
Original language | English |
---|---|
Pages (from-to) | 295-312 |
Number of pages | 18 |
Journal | Discrete and Continuous Dynamical Systems - Series B |
Volume | 18 |
Issue number | 2 |
DOIs | |
Publication status | Published - Mar 2013 |
Externally published | Yes |
Keywords
- Elliptic partial differential inclusions
- Finite element methods
- Set-valued numerical analysis
- Uncertainty quantification