Nonconforming boundary elements and finite elements for interface and contact problems with friction [Elektronische Ressource] : hp-version for mortar, penalty and Nitsche's methods / von Alexey Chernov

Nonconforming boundary elementsand finite elements for interfaceand contact problems with friction –hp-version for mortar,penalty and Nitsche’s methodsVon der Fakulta¨t fu¨r Mathematik und Physikder Universitat Hannover¨zur Erlangung des GradesDoktor der NaturwissenschaftenDr. rer. nat.genehmigte DissertationvonDipl.-Math. Alexey Chernovgeboren am 13.08.1981 in Moskau2006Referent: Prof. Dr. E. P. Stephan, Universita¨t HannoverKorreferent: Prof. Dr. P. Hansbo, Chalmers University of Technology, Go¨teborgKorreferent: Prof. Dr. J. Gwinner, Universitat der Bundeswehr, Munchen¨ ¨Tag der Promotion: 27.06.2006AbstractTheobjectiveofthisthesisistheconstruction,analysisandimplementationofhighorderFE,BEandFE/BEcoupling methods forinterface andfrictionalcontact problems withnonmatching discretizations, which have a wide industrial application.A new hp-Nitsche’s FE/BE coupling method for interface problems is designed andanalysed. The method is proven to be consistent and stable, independent of the dis-cretization parameters. A priori error analysis shows that the method is optimal in hand is suboptimal in p on quasiuniform meshes.The question of unique solvability is addressed for the one-body contact problem withTresca’s friction. Constructing a chain of equivalent formulations the frictional contactproblem is approximated with a sequence of frictionless contact problems (Uzawa algo-rithm). Conditions for the convergence of the algorithm are obtained.