In this paper, we employ a space-time finite element method to discretize the parabolic initial-boundary value problem and extend its error analysis with refined estimates on unstructured space-time meshes. We establish higher-order estimates in three different norms, thereby supplementing existing research. Moreover, we obtain an optimal estimate in a norm stronger than that of the trial space. Finally, we present numerical examples to illustrate our theoretical results.

翻译：本文采用时空有限元方法离散抛物型初边值问题，并在非结构化时空网格上通过精细化估计扩展其误差分析。我们在三种不同范数下建立了高阶估计，从而补充了现有研究。此外，我们在比试验空间范数更强的范数中获得了最优估计。最后，我们通过数值算例验证了理论结果。