We consider a linear elliptic PDE and a quadratic goal functional. The goal-oriented adaptive FEM algorithm (GOAFEM) solves the primal as well as a dual problem, where the goal functional is always linearized around the discrete primal solution at hand. We show that the marking strategy proposed in [Feischl et al, SIAM J. Numer. Anal., 54 (2016)] for a linear goal functional is also optimal for quadratic goal functionals, i.e., GOAFEM leads to linear convergence with optimal convergence rates.

中文翻译：

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具有二次目标泛函的面向目标 FEM 的最优收敛率

我们考虑线性椭圆偏微分方程和二次目标泛函。面向目标的自适应 FEM 算法 (GOAFEM) 解决了原始问题和对偶问题，其中目标泛函始终围绕手头的离散原始解决方案进行线性化。我们展示了 [Feischl 等人，SIAM J.Numer. Anal., 54 (2016)] 对于线性目标函数也是最优的二次目标函数，即 GOAFEM 导致具有最佳收敛率的线性收敛。