We develop a high-order finite element method to solve the advection-diffusion equation on a timevarying domain. The method is based on a characteristic-Galerkin formulation combined with the k th -order backward differentiation formula (BDF-k) and the fictitious-domain finite element method. Optimal error estimates of the discrete solutions are proven for 2 ≤ k ≤ 4 by taking account of the errors from interface-tracking, temporal discretization, and spatial discretization, provided that the (k + 1) th -order Runge-Kutta scheme is used for interfacetracking. Numerical experiments demonstrate the optimal convergence of the method for k = 3 and 4.

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