Galerkin finite element methods for semilinear elliptic differential inclusions

Wolf Jürgen Beyn, Janosch Rieger

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4 Citations (Scopus)


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 languageEnglish
Pages (from-to)295-312
Number of pages18
JournalDiscrete and Continuous Dynamical Systems - Series B
Issue number2
Publication statusPublished - Mar 2013
Externally publishedYes


  • Elliptic partial differential inclusions
  • Finite element methods
  • Set-valued numerical analysis
  • Uncertainty quantification

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