A Contraction Property of an Adaptive Divergence-Conforming Discontinuous Galerkin Method for the Stokes Problem
Numerical Analysis
2018-07-24 v1
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.
Keywords
Cite
@article{arxiv.1807.08623,
title = {A Contraction Property of an Adaptive Divergence-Conforming Discontinuous Galerkin Method for the Stokes Problem},
author = {Natasha Sharma and Guido Kanschat},
journal= {arXiv preprint arXiv:1807.08623},
year = {2018}
}