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arXiv · 1609.04506

Robust residual-based a posteriori error estimators for mixed finite element methods for fourth order elliptic singularly perturbed problems

Shaohong Du·Runchang Lin·Zhimin Zhang
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Abstract

We consider mixed finite element approximation of a singularly perturbed fourth-order elliptic problem with two different boundary conditions, and present a new measure of the error, whose components are balanced with respect to the perturbation parameter. Robust residual-based a posteriori estimators for the new measure are obtained, which are achieved via a novel analytical technique based on an approximation result. Numerical examples are presented to validate our theory.

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Shaohong Du, Runchang Lin, Zhimin Zhang. 2016-09-15. Robust residual-based a posteriori error estimators for mixed finite element methods for fourth order elliptic singularly perturbed problems. https://arxiv.org/abs/1609.04506

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