灵敏度权值恢复的DWR型后验误差估计的可靠性和有效性
Reliability and efficiency of DWR-type a posteriori error estimates with smart sensitivity weight recovering
摘要：
我们得到有效的和可靠的目标为导向的误差估计，并设计自适应网格程序的有限元法是基于本地化的后验估计。在我们以前的工作[SIAM J. Sci.计算：42（1），A371-A394，2020]，我们证明了基于丰富的有限元空间的误差估计的效率和可靠性。然而，在丰富的有限元空间上求解问题是昂贵的。在文献中，众所周知，可以使用一些高阶插值来克服这个瓶颈。使用饱和的假设，我们扩展的效率和可靠性的证明，这样的高阶插值。结果可以用来创建一个新的家庭的算法，其中之一是测试的三个数值例子（泊松问题，p-Laplace方程，Navier-Stokes benschmark），并与我们以前的算法。
英文摘要：
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.
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