A high-order fictitious-domain method for the advection-diffusion equation on time-varying domain
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We develop a high-order finite element method to solve the advection-diffusion equation on a time-varying 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 interface-tracking. Numerical experiments demonstrate the optimal convergence of the method for k=3 and 4.
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