This paper studies a finite element discretization of the regularized Bingham equations that describe viscoplastic flow. An efficient nonlinear solver for the discrete model is then proposed and analyzed. The solver is based on Anderson acceleration (AA) applied to a Picard iteration, and we show accelerated convergence of the method by applying AA theory (recently developed by the authors) to the iteration, after showing sufficient smoothness properties of the associated fixed point operator. Numerical tests of spatial convergence are provided, as are results of the model for 2D and 3D driven cavity simulations. For each numerical test, the proposed nonlinear solver is also tested and shown to be very effective and robust with respect to the regularization parameter as it goes to zero.

翻译：本文研究了描述离散模型的高效非线性解析器,然后提出和分析离散模型的高效非线性解析器。解析器以Anderson加速度(AA)为基础,适用于Picard迭代,我们通过将AA理论(作者最近开发的理论)应用于迭代,在显示相关固定点操作员足够平稳的特性后,显示该方法加速趋同。提供了空间趋同的数值测试,以及2D和3D驱动的轨迹模拟模型的结果。在每次数字测试中,拟议的非线性解析器也经过测试,并显示在达到零的正规化参数方面非常有效和有力。