This paper presents the numerical analysis of a stabilized finite element scheme with discontinuous Galerkin (dG) discretization in time for the solution of a transient convection–diffusion–reaction equation in time-dependent domains. In particular, the local projection stabilization and the higher order dG time stepping scheme are used for convection dominated problems. Further, an arbitrary Lagrangian–Eulerian formulation is used to handle the time-dependent domain. The stability and error estimates are given for the proposed numerical scheme. The validation of the proposed local projection stabilization scheme with higher order dG time discretization is demonstrated with appropriate numerical examples.

中文翻译：

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使用不连续伽辽金方法进行局部投影稳定，适用于瞬态域中的对流主导问题

本文介绍了具有不连续伽辽金 (dG) 离散化的稳定有限元方案的数值分析，用于求解瞬态对流-扩散-反应方程在瞬态域中。特别是，局部投影稳定和高阶 dG 时间步进方案用于对流主导问题。此外，使用任意的拉格朗日-欧拉公式来处理瞬态域。给出了所提出的数值方案的稳定性和误差估计。通过适当的数值例子证明了所提出的具有高阶 dG 时间离散化的局部投影稳定方案的验证。