In this paper a time-explicit weak Galerkin finite element method is introduced and analyzed for parabolic equations. The main idea relies on the inclusion of a stabilization term in the temporal direction in addition to the usual static stabilization in the weak Galerkin framework. Both semi-discrete and fully-discrete schemes in time are presented, as well as their stability and error analysis. Numerical results are reported for this new explicit weak Galerkin finite element method.

中文翻译：

---

多面体分区上抛物方程的时间显式弱 Galerkin 格式

本文介绍并分析了抛物线方程的时间显式弱Galerkin有限元方法。除了弱 Galerkin 框架中通常的静态稳定之外，主要思想依赖于在时间方向上包含稳定项。给出了时间上的半离散和全离散方案，以及它们的稳定性和误差分析。报告了这种新的显式弱 Galerkin 有限元方法的数值结果。