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：本文研究了抛物问题的时空目标导向后验误差估计方法。时间和空间离散化采用基于连续与不连续类型的伽辽金有限元方法。主要目标在于发展并分析基于单位分解弱形式的时空估计器局部化方法，所得误差指示因子用于时空自适应计算。通过多个数值算例验证了所提方法的有效性。