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We analyze a numerical model for the Signorini unilateral contact, based on the mortar method, in the quadratic finite element context. The mortar frame enables one to use non-matching grids and brings facilities in the mesh generation of different components of a complex system. The convergence rates we state here are similar to those already obtained for the Signorini problem when discretized on conforming meshes. The matching for the unilateral contact driven by mortars preserves then the proper...
The contact between two membranes can be described by a system of variational
inequalities, where the unknowns are the displacements of the membranes and the
action of a membrane on the other one. We first perform the analysis of this
system. We then propose a discretization, where the displacements are
approximated by standard finite elements and the action by a
local postprocessing. Such a discretization admits an equivalent mixed
reformulation. We prove the well-posedness of the discrete problem...
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