Uniform convergence and a posteriori error estimators for the enhanced strain finite element method

Authors:
D. Braess;C. Carstensen;B. D. Reddy
Affiliations:
Ruhr-University, Germany;Vienna University of Technology, Austria;University of Cape Town, South Africa
Venue:
Numerische Mathematik
Year:
2004

Citing 0
Cited 4

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L2(H1) norm a posteriori error estimation for discontinuous Galerkin approximations of reactive transport problems

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Primal mixed finite-element approximation of elliptic equations with gradient nonlinearities

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Shear Locking in a Plane Elasticity Problem and the Enhanced Assumed Strain Method

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Abstract

Enhanced strain elements, frequently employed in practice, are known to improve the approximation of standard (non-enhanced) displacement-based elements in finite element computations. The first contribution in this work towards a complete theoretical explanation for this observation is a proof of robust convergence of enhanced element schemes: it is shown that such schemes are locking-free in the incompressible limit, in the sense that the error bound in the a priori estimate is independent of the relevant Lamé constant. The second contribution is a residual-based a posteriori error estimate; the L 2 norm of the stress error is estimated by a reliable and efficient estimator that can be computed from the residuals.