Galerkin finite element methods for semilinear elliptic differential inclusions

Beyn W-J, Rieger J (2013)
Discrete And Continuous Dynamical Systems. Series B 18(2): 295-312.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor/in
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Abstract / Bemerkung
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 H-1-norm. Moreover, the solution sets of the Galerkin inclusion converge with respect to the Hausdorff distance measured in L-p-spaces.
Stichworte
uncertainty quantification; Elliptic partial differential inclusions; finite element methods; set-valued numerical analysis
Erscheinungsjahr
2013
Zeitschriftentitel
Discrete And Continuous Dynamical Systems. Series B
Band
18
Ausgabe
2
Seite(n)
295-312
ISSN
1531-3492
Page URI
https://pub.uni-bielefeld.de/record/2553220

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Beyn W-J, Rieger J. Galerkin finite element methods for semilinear elliptic differential inclusions. Discrete And Continuous Dynamical Systems. Series B. 2013;18(2):295-312.
Beyn, W. - J., & Rieger, J. (2013). Galerkin finite element methods for semilinear elliptic differential inclusions. Discrete And Continuous Dynamical Systems. Series B, 18(2), 295-312. doi:10.3934/dcdsb.2013.18.295
Beyn, W. - J., and Rieger, J. (2013). Galerkin finite element methods for semilinear elliptic differential inclusions. Discrete And Continuous Dynamical Systems. Series B 18, 295-312.
Beyn, W.-J., & Rieger, J., 2013. Galerkin finite element methods for semilinear elliptic differential inclusions. Discrete And Continuous Dynamical Systems. Series B, 18(2), p 295-312.
W.-J. Beyn and J. Rieger, “Galerkin finite element methods for semilinear elliptic differential inclusions”, Discrete And Continuous Dynamical Systems. Series B, vol. 18, 2013, pp. 295-312.
Beyn, W.-J., Rieger, J.: Galerkin finite element methods for semilinear elliptic differential inclusions. Discrete And Continuous Dynamical Systems. Series B. 18, 295-312 (2013).
Beyn, Wolf-Jürgen, and Rieger, Janosch. “Galerkin finite element methods for semilinear elliptic differential inclusions”. Discrete And Continuous Dynamical Systems. Series B 18.2 (2013): 295-312.