This paper aims to study a degenerate parabolic problem for a solenoidal vector field in which the time derivative acts on a moving body. We propose a fully-discrete finite element scheme combined with backward Euler’s method for the saddle-point variational formulation. The convergence of this numerical scheme is proved and error estimates for some stable finite element pairs are also established.

中文翻译：

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涉及运动体的退化抛物线问题的鞍点方法的完全离散化

本文旨在研究时间导数作用于运动体的螺线管矢量场的退化抛物线问题。我们提出了一种完全离散的有限元方案，并结合了用于鞍点变分公式的后向欧拉方法。证明了该数值方案的收敛性，并建立了一些稳定有限元对的误差估计。