Affiliation:
1. Fakultät für Mathematik , Universität Duisburg–Essen , Thea-Leymann-Str. 9, 45127 Essen , Germany
Abstract
Abstract
The nonconforming triangular piecewise quadratic finite element space by Fortin and Soulie can be used for the displacement
approximation and its combination with discontinuous piecewise linear pressure elements is known to constitute a stable
combination for incompressible linear elasticity computations. In this contribution, we extend the stress reconstruction
procedure and resulting guaranteed a posteriori error estimator developed by Ainsworth, Allendes, Barrenechea and Rankin
[2] and by Kim [18] to linear elasticity. In order to get a guaranteed reliability bound with respect
to the energy norm involving only known constants, two modifications are carried out: (i) the stress reconstruction in
next-to-lowest order Raviart–Thomas spaces is modified in such a way that its anti-symmetric part vanishes in average on each
element; (ii) the auxiliary conforming approximation is constructed under the constraint that its divergence coincides with the
one for the nonconforming approximation. An important aspect of our construction is that all results hold uniformly in the
incompressible limit. Global efficiency is also shown and the effectiveness is illustrated by adaptive computations
involving different Lamé parameters including the incompressible limit case.
Subject
Applied Mathematics,Computational Mathematics,Numerical Analysis
Cited by
10 articles.
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