A Fourth-Order Unfitted Characteristic Finite Element Method for Solving the Advection-Diffusion Equation on Time-Varying Domains

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