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 $L^2(\Omega)$-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.
翻译:我们建议对笛卡尔的二次树叶色色片采用网状适应程序,以分解电弧反向扩散反应问题。适应过程由基于回收的离散错误的事后估计值驱动,该估计值为$L2 (\\ Omega)$-norm,其依据是解决方案和相关梯度的适当的更高排序近似值。特别是,基于指标的方法利用测量仪提供的信息对新的经调整的网状进行迭接预测。新的网状适应算法在不同的配置上得到成功评估,在处理数据不连续以及内部层与卡尔提斯方向不相一致时,该算法也表现良好。与标准估计-标记-雷芬办法和文献中的其他适应战略的交叉比较表明拟议方法的惊人准确性和平行的可扩展性。