Abstract We consider an adaptive finite element method with arbitrary but fixed polynomial degree p ≥ 1 {p\geq 1} , where adaptivity is driven by an edge-based residual error estimator. Based on the modified maximum criterion from [L. Diening, C. Kreuzer and R. Stevenson, Instance optimality of the adaptive maximum strategy, Found. Comput. Math. 16 2016, 1, 33–68], we propose a goal-oriented adaptive algorithm and prove that it is instance optimal. More precisely, the goal error is bounded by the product of the total errors (being the sum of energy error plus data oscillations) of the primal and the dual problem, and the proposed algorithm is instance optimal with respect to this upper bound. Numerical experiments underline our theoretical findings.

中文翻译：

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实例最优的面向目标的自适应

摘要 我们考虑具有任意但固定多项式次数 p ≥ 1 {p\geq 1} 的自适应有限元方法，其中自适应性由基于边缘的残差估计器驱动。基于 [L. Diening、C. Kreuzer 和 R. Stevenson，自适应最大策略的实例最优性，Found。计算。数学。16 2016, 1, 33–68]，我们提出了一种面向目标的自适应算法并证明它是实例最优的。更准确地说，目标误差受原始问题和对偶问题的总误差的乘积（即能量误差加上数据振荡的总和）的限制，并且所提出的算法对于该上限是实例最优的。数值实验强调了我们的理论发现。