论文标题
张量产品时空面向目标的误差控制和适应性，并分配了非组织流量问题的单一双重加权残差
Tensor-product space-time goal-oriented error control and adaptivity with partition-of-unity dual-weighted residuals for nonstationary flow problems
论文作者
论文摘要
在这项工作中，双重加权剩余方法应用于非平稳性Stokes和Navier-Stokes流的时空公式。张量产品时空有限元元素被用来在时间上使用不连续的Galerkin有限元元素和空间中的inf-sup稳定的泰勒 - 泰勒·霍德有限元对离散。为了估算一定兴趣和驱动时间和空间中的自适应改进的误差，我们演示了如何将双重加权的残留方法扩展到基于统一的错误定位的分区。我们得出了Navier-Stokes方程的时空牛顿方法，并证实了我们从计算流体力学中的2D基准问题的方法。
In this work, the dual-weighted residual method is applied to a space-time formulation of nonstationary Stokes and Navier-Stokes flow. Tensor-product space-time finite elements are being used to discretize the variational formulation with discontinuous Galerkin finite elements in time and inf-sup stable Taylor-Hood finite element pairs in space. To estimate the error in a quantity of interest and drive adaptive refinement in time and space, we demonstrate how the dual-weighted residual method for incompressible flow can be extended to a partition of unity based error localization. We derive the space-time Newton method for the Navier-Stokes equations and substantiate our methodology on 2D benchmark problems from computational fluid mechanics.
