论文标题
具有二次目标功能的目标FEM的最佳收敛率
Optimal convergence rates for goal-oriented FEM with quadratic goal functional
论文作者
论文摘要
我们考虑线性椭圆PDE和二次目标功能。面向目标的自适应FEM算法（GOAFEM）解决了原始问题和双重问题，在该问题中，目标功能始终围绕手头的离散原始解决方案进行线性性。我们表明，[Feischl等人，Siam J. Numer中提出的标记策略。对于线性目标功能，肛门，54（2016）]对于二次目标功能也是最佳的，即，果Afem会导致以最佳收敛速率线性收敛。
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.
