TY - GEN A1 - Knees, Dorothee A1 - Schröder, Andreas T1 - Global spatial regularity for elasticity models with cracks, contact and other nonsmooth constraints N2 - A global higher differentiability result in Besov spaces is proved for the displacement fields of linear elastic models with self contact. Domains with cracks are studied, where nonpenetration conditions/Signorini conditions are imposed on the crack faces. It is shown that in a neighborhood of crack tips (in 2D) or crack fronts (3D) the displacement fields are $B^{3/2}_{2,\infty}$ regular. The proof relies on a difference quotient argument for the directions tangential to the crack. In order to obtain the regularity estimates also in the normal direction, an argument due to Ebmeyer/Frehse/Kassmann is modified. The methods are then applied to further examples like contact problems with nonsmooth rigid foundations, to a model with Tresca friction and to minimization problems with nonsmooth energies and constraints as they occur for instance in the modeling of shape memory alloys. Based on Falk's approximation Theorem for variational inequalities, convergence rates for FE-discretizations of contact problems are derived relying on the proven regularity properties. Several numerical examples illustrate the theoretical results. KW - global spatial regularity KW - cracks with selfcontact KW - Signorini contact KW - difference quotient KW - Tresca friction KW - finite elements KW - a priori error analysis Y1 - 2012 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/954 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-9544 ER -