We propose a $k^{\rm th}$-order unfitted finite element method ($2\le k\le 4$) to solve the moving interface problem of the Oseen equations. Thorough error estimates for the discrete solutions are presented by considering errors from interface-tracking, time integration, and spatial discretization. In literatures on time-dependent Stokes interface problems, error estimates for the discrete pressure are usually sub-optimal, namely, $(k-1)^{\rm th}$-order, under the $L^2$-norm. We have obtained a $(k-1)^{\rm th}$-order error estimate for the discrete pressure under the $H^1$-norm. Numerical experiments for a severely deforming interface show that optimal convergence orders are obtained for $k = 3$ and $4$.
翻译：我们建议使用$k ⁇ rm th}$-顺序不适的有限要素法(2\le k\le 4美元)解决Oseen方程式的移动界面问题。通过考虑接口跟踪、时间整合和空间离散的错误,可以提出离散解决方案的彻底错误估计。在关于时间依赖的斯托克斯界面问题的文献中,离散压力的错误估计通常是次最佳的,即$(k-1) {rm th}-顺序,在$L2$-norm下。我们已经获得了1美元-norm下的离散压力的(k-1) $-rm rth} 顺序错误估计。严重变形接口的数值实验显示,美元=3美元和4美元是最佳的趋同订单。
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