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A Contraction Property of an Adaptive Divergence-Conforming Discontinuous Galerkin Method for the Stokes Problem
Journal of Numerical Mathematics ( IF 3 ) Pub Date : 2018-12-19 , DOI: 10.1515/jnma-2016-1132
Natasha Sharma , Guido Kanschat

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.

中文翻译:

斯托克斯问题的自适应发散一致不连续伽辽金方法的收缩性质

摘要 我们证明了斯托克斯问题自适应算法在两个连续循环中的收缩性质,减少了速度误差。该问题通过符合发散的不连续 Galerkin 方法离散化,该方法由于其 cochain 属性而将压力和速度近似分开。这使我们能够建立准正交性,这对于证明收缩至关重要。我们还根据自由度建立了自适应算法的准最优复杂度。
更新日期:2018-12-19
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