广义$p$ -Stokes粘塑性流动问题Huber正则化的对偶混合逼近
A Dual-Mixed Approximation for a Huber Regularization of Generalized $p$-Stokes Viscoplastic Flow Problems
摘要：
在本文中，我们提出了一个双重混合列式的定常粘塑性流动的屈服，如宾厄姆或赫歇尔-Bulkley流。该方法是基于Huber正则化的粘性项和一个双重鞍点非线性算子方程的弱制定。我们提供了解决方案的唯一性的连续配方，并提出了一个离散的计划的基础上Arnold-Falk-Winther有限元。离散方案产生一个系统的斜可微的非线性方程，其中的半光滑牛顿算法的建议和实施。证明了该方法的局部超线性收敛。最后，我们在二维和三维进行了几个数值实验，以研究该方法的行为和效率。
英文摘要：
In this paper, we propose a dual-mixed formulation for stationary viscoplastic flows with yield, such as the Bingham or the Herschel-Bulkley flow. The approach is based on a Huber regularization of the viscosity term and a two-fold saddle point nonlinear operator equation for the resulting weak formulation. We provide the uniqueness of solutions for the continuous formulation and propose a discrete scheme based on Arnold-Falk-Winther finite elements. The discretization scheme yields a system of slantly differentiable nonlinear equations, for which a semismooth Newton algorithm is proposed and implemented. Local superlinear convergence of the method is also proved. Finally, we perform several numerical experiments in two and three dimensions to investigate the behavior and efficiency of the method.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
