For the pure biharmonic equation and a biharmonic singular perturbation problem, a residual-based error estimator is introduced which applies to many existing nonconforming finite elements. The error estimator involves the local best-approximation error of the finite element function by piecewise polynomial functions of the degree determining the expected approximation order, which need not coincide with the maximal polynomial degree of the element, for example if bubble functions are used. The error estimator is shown to be reliable and locally efficient up to this polynomial best-approximation error and oscillations of the right-hand side.

翻译：针对纯双调和方程及双调和奇异摄动问题，本文提出了一种基于残差的误差估计子，该估计子适用于多种现有的非协调有限元。该误差估计子涉及有限元函数通过分片多项式函数产生的局部最优逼近误差，其中多项式的次数决定了预期的逼近阶，该次数不必与单元的最大多项式次数一致（例如，当采用泡函数时）。误差估计子被证明是可靠的，并且局部有效，其有效性仅受该多项式最优逼近误差及右端项振荡的影响。