论文标题
面向目标的自适应FEM的平原收敛
Plain convergence of goal-oriented adaptive FEM
论文作者
论文摘要
我们在符合有限元方法的框架中讨论了面向目标的适应性，并针对不同的一般标记策略的后验误差估计器的平淡收敛。我们为两个不同的设置提供了抽象分析。首先，我们考虑当地离散效率估计的问题。其次，我们在仅依赖于误差估计器的结构特性的环境中表现出平淡的收敛性，即对未精制元素的稳定性以及精制元素的降低。特别是，第二个设置不需要可靠性和效率估算。数值实验强调了我们的理论发现。
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.
