We present new constructions of (approximate) H(div, Ω)-liftings of the algebraic residual leading to estimators of the algebraic error in h and p finite element discretizations of a model diffusion problem. The estimators provide guaranteed bounds without any uncomputable constants and they are globally efficient, similarly to some recent developments, but the cost of their construction is significantly reduced. We provide a set of numerical experiments to assess the performance of the new estimators.

中文翻译：

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有限元离散化中代数误差的廉价保证和有效上限

我们提出了代数残差的（近似）H (div, Ω ) 提升的新构造，导致模型扩散问题的h和p有限元离散化中的代数误差的估计。估计器提供有保证的边界，没有任何不可计算的常数，并且它们是全局有效的，类似于最近的一些发展，但它们的构建成本显着降低。我们提供了一组数值实验来评估新估计器的性能。