标题： 各向异性时空目标误差控制与对流扩散反应方程的网格自适应 显示英文标题

标题： Anisotropic space-time goal-oriented error control and mesh adaptivity for convection-diffusion-reaction equations

摘要： 我们提出了一种基于时间相关的对流扩散反应（CDR）方程的Dual Weighted Residual (DWR) 方法的各向异性目标误差估计器。通过使用各向异性插值算子，该估计器在空间和时间的单个方向上被逐单元分离，从而自然地导致自适应的各向异性网格细化。为了防止虚假振荡，在高Péclet数的情况下，应用了流线迎风Petrov-Galerkin (SUPG) 方法来稳定基础系统。对于不同的目标泛函，展示了底层算法的有效性和鲁棒性。方向误差指示器量化了解决方案相对于目标的各向异性，并生成能够有效捕获尖锐层的网格。数值例子表明，所提出的方法优于各向同性和全局网格细化方法，并且使用了对流占优传输的经典基准测试。 显示英文摘要

摘要： We present an anisotropic goal-oriented error estimator based on the Dual Weighted Residual (DWR) method for time-dependent convection-diffusion-reaction (CDR) equations. Using anisotropic interpolation operators the estimator is elementwise separated with respect to the single directions in space and time leading to adaptive, anisotropic mesh refinement in a natural way. To prevent spurious oscillations the streamline upwind Petrov-Galerkin (SUPG) method is applied to stabilize the underlying system in the case of high P\'eclet numbers. Efficiency and robustness of the underlying algorithm are demonstrated for different goal functionals. The directional error indicators quantify anisotropy of the solution with respect to the goal, and produce meshes that efficiently capture sharp layers. Numerical examples show the superiority of the proposed approach over isotropic adaptive and global mesh refinement using established benchmarks for convection-dominated transport.