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arXiv · 1807.08623

A Contraction Property of an Adaptive Divergence-Conforming Discontinuous Galerkin Method for the Stokes Problem

Natasha Sharma·Guido Kanschat
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Abstract

We prove the contraction property for two successive loops of the adaptive algorithm for the Stokes problem reducing the error of the velocity. The problem is discretized by a divergence-conforming discontinuous Galerkin method which separates pressure and velocity approximation due to its cochain property. This allows us to establish the quasi-orthogonality property which is crucial for the proof of the contraction. We also establish the quasi-optimal complexity of the adaptive algorithm in terms of the degrees of freedom.

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Natasha Sharma, Guido Kanschat. 2018-07-23. A Contraction Property of an Adaptive Divergence-Conforming Discontinuous Galerkin Method for the Stokes Problem. https://doi.org/10.1515/jnma-2016-1132

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