We propose a fourth-order unfitted characteristic finite element method to solve the advection-diffusion equation on time-varying domains. Based on a characteristic-Galerkin formulation, our method combines the cubic MARS method for interface tracking, the fourth-order backward differentiation formula for temporal integration, and an unfitted finite element method for spatial discretization. Our convergence analysis includes errors of discretely representing the moving boundary, tracing boundary markers, and the spatial discretization and the temporal integration of the governing equation. Numerical experiments are performed on a rotating domain and a severely deformed domain to verify our theoretical results and to demonstrate the optimal convergence of the proposed method.

翻译：我们建议了一种第四顺序不适合的特性有限要素方法,用以解决时间变化域的平面反扩散方程式。根据一种特性-伽勒金公式,我们的方法结合了连接跟踪的立方MARS方法、时间整合的四阶后向差异公式和空间分化的不适的有限要素方法。我们的趋同分析包括分代表移动边界、追踪界标、空间分解和调节方程式的时间整合的错误。数字实验是在一个旋转域进行,一个严重畸形的域进行,以核实我们的理论结果并展示拟议方法的最佳趋同。