Error control by means of a posteriori error estimators or indica-tors and adaptive discretizations, such as adaptive mesh refinement, have emerged in the late seventies. Since then, numerous theoretical developments and improvements have been made, as well as the first attempts to introduce them into real-life industrial applications. The present introductory chapter provides an overview of the subject, highlights some of the achievements to date and discusses possible perspectives.

翻译：后验误差估计器或指示器以及自适应离散化（如自适应网格细化）于七十年代末兴起。此后，该领域在理论发展与改进方面取得了丰硕成果，并已初步尝试应用于实际工业场景。本章作为引言，将概述该主题的研究脉络，重点总结当前取得的若干进展，并探讨其未来可能的发展方向。