论文标题
对流扩散反应问题的Quadtree网格的可扩展基于恢复的适应
Scalable Recovery-based Adaptation on Quadtree Meshes for Advection-Diffusion-Reaction Problems
论文作者
论文摘要
我们提出了针对笛卡尔四分之一网格的网格适应程序，以使标量对流 - 扩散反应问题离散。适应过程是由基于$ l^2（ω）$ - 离散误差的标准的基于恢复的后验估计器驱动的，基于解决方案和相关梯度的适当高阶近似值。特别是，一种基于度量的方法利用估计器提供的信息迭代预测了新的改装网格。新的网格适应算法已成功地评估了不同的配置，并且在处理数据中的不连续性以及在与笛卡尔方向不符的内部图层的存在下，还表现良好。与标准估计值的交叉比较 - 标记 - 雷丁方法以及文献中其他可用的自适应策略显示了所提出方法的显着准确性和并行的可伸缩性。
We propose a mesh adaptation procedure for Cartesian quadtree meshes, to discretize scalar advection-diffusion-reaction problems. The adaptation process is driven by a recovery-based a posteriori estimator for the $L^2(Ω)$-norm of the discretization error, based on suitable higher order approximations of both the solution and the associated gradient. In particular, a metric-based approach exploits the information furnished by the estimator to iteratively predict the new adapted mesh. The new mesh adaptation algorithm is successfully assessed on different configurations, and turns out to perform well also when dealing with discontinuities in the data as well as in the presence of internal layers not aligned with the Cartesian directions. A cross-comparison with a standard estimate--mark--refine approach and with other adaptive strategies available in the literature shows the remarkable accuracy and parallel scalability of the proposed approach.
