An abstract property (H) is the key to a complete a priori error analysis in the (discrete) energy norm for several nonstandard finite element methods in the recent work [Lowest-order equivalent nonstandard finite element methods for biharmonic plates, Carstensen and Nataraj, M2AN, 2022]. This paper investigates the impact of (H) to the a posteriori error analysis and establishes known and novel explicit residualbased a posteriori error estimates. The abstract framework applies to Morley, two versions of discontinuous Galerkin, C 0 interior penalty, as well as weakly overpenalized symmetric interior penalty schemes for the biharmonic equation with a general source term in H −2(Ω).

中文翻译：

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统一双调和方程的五个分段二次离散化的后验误差分析

抽象属性 (H) 是近期工作中几种非标准有限元方法的（离散）能量范数中完整先验误差分析的关键 [双调和板的最低阶等效非标准有限元方法，Carstensen 和 Nataraj， M2AN，2022]。本文研究了 (H) 对后验误差分析的影响，并建立了已知的和新颖的基于显式残差的后验误差估计。抽象框架适用于 Morley，不连续 Galerkin 的两个版本，C 0内部惩罚，以及具有一般源项的双调和方程的弱过度惩罚对称内部惩罚方案H −2（Ω）。