Mixed finite element methods for two-body contact problems

Andreas Schröder ^[1] ; Heiko Kleemann ^[3] ; Heribert Blum ^[2]
1. [1] University of Salzburg
  
  University of Salzburg
  
  Salzburg, Austria
2. [2] Technical University of Dortmund
  
  Technical University of Dortmund
  
  Kreisfreie Stadt Dortmund, Alemania
3. [3] echnische Universität Dortmund, Germany
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Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 283, Nº 1 (1 August 2015), 2015, págs. 58-70
Idioma: inglés
DOI: 10.1016/j.cam.2014.11.040
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Resumen
- This paper presents mixed finite element methods of higher-order for two-body contact problems of linear elasticity. The discretization is based on a mixed variational formulation proposed by Haslinger et al. which is extended to higher-order finite elements. The main focus is on the convergence of the scheme and on a priori estimates for the hh- and the pp-method. For this purpose, a discrete inf–sup condition is proven which guarantees the stability of the mixed method. Numerical results confirm the theoretical findings.