An element based adaptation method is developed for an anisotropic aposteriori error estimator. The adaptation does not make use of a metric, butinstead equidistributes the error over elements using local mesh modifications.Numerical results are reported, comparing with three popular anisotropicadaptation methods currently in use. It was found that the new method givesfavourable results for controlling the energy norm of the error in terms ofdegrees of freedom at the cost of increased CPU usage. Additionally, weconsidered a new $L^2$ variant of the estimator. The estimator is shown to beconditionally equivalent to the exact $L^2$ error. We provide examples ofadapted meshes with the $L^2$ estimator, and show that it gives greater controlof the $L^2$ error compared with the original estimator.
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机译：针对各向异性的后验误差估计器，开发了一种基于元素的自适应方法。改编不使用度量，而是使用局部网格修改将误差平均分配到元素上。与目前使用的三种流行的各向异性改编方法相比，报告了数值结果。已经发现，该新方法以自由度方面为控制误差的能量范数提供了有利的结果，但代价是增加了CPU使用率。此外，我们还考虑了估算器的新的$ L ^ 2 $变体。估计器显示为有条件地等效于确切的$ L ^ 2 $误差。我们提供了带有$ L ^ 2 $估计量的自适应网格的示例，并表明与原始估计量相比，它可以更好地控制$ L ^ 2 $误差。
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