For pixel-based microstructure representations we propose two different variants of adaptive, quadtree-based mesh coarsening algorithms that serve the purpose of a preprocessor for finite element analyses in the context of numerical homogenization. High resolution is preserved at interfaces for accuracy, coarse-graining in the defect-free interior of phases for efficiency. Error analysis is carried out on the micro scale by error estimation which itself is assessed by true error computation. Modified stress recovery schemes for an error indicator are proposed which overcome the deficits of the standard superconvergent recovery scheme for nodal stress computation in cases of interfaces with stiffness jump. By virtue of error analysis the improved efficiency by the reduction of unknowns is put into relation to the increase of the discretization error and thereby sets a rational basis for decisions on favorable meshes having the best trade-off between accuracy and efficiency as underpinned by various examples.

中文翻译：

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适应像素化异质微结构的四叉树型网格粗化算法的误差分析

对于基于像素的微观结构表示，我们提出了两种不同的自适应、基于四叉树的网格粗化算法变体，它们在数值均匀化的背景下用于有限元分析的预处理器。在界面处保留高分辨率以提高准确性，在相的无缺陷内部保留粗粒度以提高效率。误差分析是通过误差估计在微观尺度上进行的，误差估计本身是通过真实误差计算来评估的。提出了用于误差指标的修正应力恢复方案，该方案克服了在具有刚度跳跃的界面的情况下节点应力计算的标准超收敛恢复方案的缺陷。