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arXiv · 1409.0563

Trace and flux a priori error estimates in finite element approximations of Signorni-type problems

Olaf Steinbach·Barbara Wohlmuth·Linus Wunderlich
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Abstract

Variational inequalities play in many applications an important role and are an active research area. Optimal a priori error estimates in the natural energy norm do exist but only very few results in other norms exist. Here we consider as prototype a simple Signorini problem and provide new optimal order a priori error estimates for the trace and the flux on the Signorini boundary. The a priori analysis is based on the exact and a mesh-dependent Steklov-Poincar\'e operator as well as on duality in Aubin-Nitsche type arguments. Numerical results illustrate the convergence rates of the finite element approach.

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Olaf Steinbach, Barbara Wohlmuth, Linus Wunderlich. 2014-09-01. Trace and flux a priori error estimates in finite element approximations of Signorni-type problems. https://doi.org/10.1093/imanum/drv039

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