我们考虑一个线性椭圆型偏微分方程和一个二次目标泛函。面向目标的自适应有限元算法（GOAFEM）解决了原始问题以及对偶问题，其中目标泛函总是围绕手头的离散原始解线性化。我们表明，在[Feischl等人，SIAM J. Numer.肛门，54（2016）]对于二次目标泛函也是最优的，即，GOAFEM导致线性收敛，具有最佳的收敛速度。
英文摘要：
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.
Veamy: an extensible object-oriented C++ library for the virtual element method
Universidad de Chile（智利大学）；Università di Milano-Bicocca（米兰比可卡大学）；Istituto di Matematica Applicata e Tecnologie Informatiche del CNR（意大利国家研究委员会应用数学与信息技术研究所）
A FEM approximation of a two-phase obstacle problem and its a posteriori error estimate
Instituto Superior Técnico（技术研究所）；University of South Bohemia（南波希米亚大学）；Institute of Information Theory and Automation, Academy of Sciences（科学院信息与自动化研究所）
Goal-Oriented Adaptive Finite Element Multilevel Quasi-Monte Carlo
King Fahd University of Petroleum and Minerals（国王法赫德石油矿物大学）；King Abdullah University of Science and Technology (KAUST)（阿卜杜拉国王科技大学）；RWTH Aachen University（亚琛工业大学）
