In this work, we consider space-time goal-oriented a posteriori error estimation for parabolic problems. Temporal and spatial discretizations are based on Galerkin finite elements of continuous and discontinuous type. The main objectives are the development and analysis of space-time estimators, in which the localization is based on a weak form employing a partition-of-unity. The resulting error indicators are used for temporal and spatial adaptivity. Our developments are substantiated with several numerical examples.

翻译：在这项工作中,我们认为时间目标为时,是对抛物线问题的事后误差估计。时空和空间离散以连续和不连续类型的Galerkin有限要素为基础,主要目标是开发和分析时空估计器,其中定位基于使用统一分配的薄弱形式。由此产生的误差指标用于时间和空间的适应性。我们的发展以若干数字实例为根据。