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The state problem of elasto-plasticity (for the model with strain-hardening) is formulated in terms of stresses and hardening parameters by means of a time-dependent variational inequality. The optimal design problem is to find the shape of a part of the boundary such that a given cost functional is minimized. For the approximate solutions piecewise linear approximations of the unknown boundary, piecewise constant triangular elements for the stress and the hardening parameter, and backward differences...
We propose and examine a simple averaging formula for the gradient of linear finite elements in whose interpolation order in the -norm is for and nonuniform triangulations. For elliptic problems in we derive an interior superconvergence for the averaged gradient over quasiuniform triangulations. A numerical example is presented.
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