Schwarz, Alexander; Schröder, Jörg; Starke, Gerhard:
Least-squares mixed finite elements for small strain elasto-viscoplasticity
2009
In: International Journal for Numerical Methods in Engineering, Jg. 77 (2009), Heft 10, S. 1351 - 1370
Artikel/Aufsatz in Zeitschrift / Fach: Bauwissenschaften
Titel:
Least-squares mixed finite elements for small strain elasto-viscoplasticity
Autor(in):
Schwarz, Alexander im Online-Personal- und -Vorlesungsverzeichnis LSF anzeigen; Schröder, Jörg im Online-Personal- und -Vorlesungsverzeichnis LSF anzeigen; Starke, Gerhard
Erscheinungsjahr
2009
Erschienen in:
International Journal for Numerical Methods in Engineering, Jg. 77 (2009), Heft 10, S. 1351 - 1370
ISSN
DOI
Signatur der UB

Abstract:

The main aim of this contribution is to provide a mixed finite element for small strain elasto-viscoplastic material behavior based on the least-squares method. The L2-norm minimization of the residuals of the given first-order system of differential equations leads to a two-field functional with displacements and stresses as process variables. For the continuous approximation of the stresses, lowest-order Raviart–Thomas elements are used, whereas for the displacements, standard conforming elements are employed. It is shown that the non-linear least-squares functional provides an a posteriori error estimator, which establishes ellipticity of the proposed variational approach. Further on, details about the implementation of the least-squares mixed finite elements are given and some numerical examples are presented.