论文标题
DWR型的可靠性和效率A后验错误估计，智能敏感性重量恢复
Reliability and efficiency of DWR-type a posteriori error estimates with smart sensitivity weight recovering
论文作者
论文摘要
我们得出了有效且可靠的面向目标误差估计，并根据后验估计的定位设计有限元方法的自适应网格程序。在我们以前的作品中[Siam J. Sci。 Comput。，42（1），A371 - A394，2020]，我们根据富含有限元空间的误差估计器显示出效率和可靠性。但是，在丰富的有限元空间上解决问题的解决方案很昂贵。在文献中，众所周知，人们可以使用一些高阶插值来克服这种瓶颈。使用饱和假设，我们将效率和可靠性的证明扩展到了这样的高阶插值。结果可用于创建一个新的算法系列，其中其中一个在三个数值示例（泊松问题，p-laplace方程，navier-stokes benschmark）上进行了测试，并与我们以前的算法进行了比较。
We derive efficient and reliable goal-oriented error estimations, and devise adaptive mesh procedures for the finite element method that are based on the localization of a posteriori estimates. In our previous work [SIAM J. Sci. Comput., 42(1), A371--A394, 2020], we showed efficiency and reliability for error estimators based on enriched finite element spaces. However, the solution of problems on a enriched finite element space is expensive. In the literature, it is well known that one can use some higher-order interpolation to overcome this bottleneck. Using a saturation assumption, we extend the proofs of efficiency and reliability to such higher-order interpolations. The results can be used to create a new family of algorithms, where one of them is tested on three numerical examples (Poisson problem, p-Laplace equation, Navier-Stokes benschmark), and is compared to our previous algorithm.
