Advances in Computational Mathematics ( IF 1.7 ) Pub Date : 2021-10-15 , DOI: 10.1007/s10444-021-09906-2 Tomás P. Barrios 1 , Edwin M. Behrens 2 , Rommel Bustinza 3
In this work, we focus our attention in the Stokes flow with nonhomogeneous source terms, formulated in dual mixed form. For the sake of completeness, we begin recalling the corresponding well-posedness at continuous and discrete levels. After that, and with the help of a kind of a quasi-Helmholtz decomposition of functions in H(div), we develop a residual type a posteriori error analysis, deducing an estimator that is reliable and locally efficient. Finally, we provide numerical experiments, which confirm our theoretical results on the a posteriori error estimator and illustrate the performance of the corresponding adaptive algorithm, supporting its use in practice.
中文翻译:
应用于具有非零源项的 Stokes 系统的对偶混合方法的后验误差估计
在这项工作中,我们将注意力集中在具有非齐次源项的斯托克斯流上,以双重混合形式表示。为了完整起见,我们开始在连续和离散级别上回顾相应的适定性。之后,在H ( d i v )中函数的一种准亥姆霍兹分解的帮助下,我们开发了一种残差类型的后验误差分析,推导出了一个可靠且局部有效的估计量。最后,我们提供了数值实验,证实了我们在后验误差估计器上的理论结果,并说明了相应自适应算法的性能,支持其在实践中的使用。