Projection Methods For Contact Problems In Elasticity

The aim of the paper is showing, how projection methods can be used for computing contact-problems in elasticity for different classes of obstacles. Starting with the projection idea for handling hanging nodes in finite element discretizations the extension of the method for handling penetrated nodes in contact problems will be described for some obstacle classes

The Giant Component Threshold for Random Regular Graphs with Edge Faults

. Let G be a given graph (modelling a communication network) which we assume suffers from static edge faults: That is we let each edge of G be present independently with probability p (or absent with fault probability f = 1 \Gamma p). In particular we are interested in robustness results for the case that the graph G itself is a random member of the class of all regular graphs with given degree. Our result is: If the degree d is fixed then p = 1=(d \Gamma 1) is a threshold probability for the existence of a linear-sized component in a faulty version of almost all random regular graphs. We show: If each edge of an arbitrary graph G with maximum degree bounded above by d is present with probability p = =(d \Gamma 1) where ! 1 is fixed then the faulted version of G has only components whose size is at most logarithmic in the number of nodes with high probability. If on the other hand G is a random regular graph with degree d and p = =(d \Gamma 1) where ? 1 then for almost all G the fault..