We discuss goal-oriented adaptivity in the frame of conforming finite element methods and plain convergence of the related a posteriori error estimator for different general marking strategies. We present an abstract analysis for two different settings. First, we consider problems where a local discrete efficiency estimate holds. Second, we show plain convergence in a setting that relies only on structural properties of the error estimators, namely stability on non-refined elements as well as reduction on refined elements. In particular, the second setting does not require reliability and efficiency estimates. Numerical experiments underline our theoretical findings.

翻译：我们讨论了在协调有限元框架下的面向目标自适应性，以及针对不同通用标记策略的相关后验误差估计子的朴素收敛性。针对两种不同设定，我们提出了一种抽象分析。首先，我们考虑局部离散效率估计成立的问题。其次，我们在仅依赖误差估计子结构性质的设定下证明了朴素收敛性，即非细化单元上的稳定性以及细化单元上的缩减性。特别地，第二种设定不要求可靠性和效率估计。数值实验验证了我们的理论结果。