The dual consistency, which is an important issue in developing dual-weighted residual error estimation towards the goal-oriented mesh adaptivity, is studied in this paper both theoretically and numerically. Based on the Newton-GMG solver, dual consistency had been discussed in detail to solve the steady Euler equations. Theoretically, based on the Petrov-Galerkin method, the primal and dual problems, as well as the dual consistency, are deeply studied. It is found that dual consistency is important both for error estimation and stable convergence rate for the quantity of interest. Numerically, through the boundary modification technique, dual consistency can be guaranteed for the problem with general configuration. The advantage of taking care of dual consistency on the Newton-GMG framework can be observed clearly from numerical experiments, in which an order of magnitude savings of mesh grids can be expected for calculating the quantity of interest, compared with the dual-inconsistent implementation. Besides, the convergence behavior from the dual-consistent algorithm is stable, which guarantees the precisions would be better with the refinement in this framework.
翻译:本文件从理论上和数字上研究了双重一致性,这是对面向目标的网格适应性进行双重加权剩余误差估计的一个重要问题。根据牛顿-GGG求解器,对双重一致性进行了详细讨论,以解决稳定的Euler方程式。理论上,根据Petrov-Galerkin方法,对原始和双重问题以及双重一致性进行了深入研究。发现双重一致性对于误差估计和利息数额的稳定趋同率都很重要。通过边界修改技术,可以保证问题在整体配置上的双重一致性。从数字实验中可以清楚地看到注意牛顿-GGGG框架的双重一致性的优势,在计算利息数量时,与双重不一致的执行相比,预期可以节省大量网格。此外,双重一致算法的趋同行为是稳定的,这保证了这个框架的完善性。</s>