A high-order unfitted finite element method for moving interface problems
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We propose a k^ th-order unfitted finite element method (2≤ k≤ 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)^ th-order, under the L^2-norm. We have obtained a (k-1)^ 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.
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