(untitled) (Journal of Computational Mathematics, 2022)
This article concerns numerical approximation of a parabolic interface problem with general L^2 initial value. The problem is discretized by a finite element method with a quasi-uniform triangulation of the domain fitting the interface, with piecewise linear approximation to the interface. The semi-discrete finite element problem is furthermore discretized in time by the k-step backward difference formula with k=1,…,6 . To maintain high-order convergence in time for possibly nonsmooth L^2 initial value, we modify the standard backward difference formula at the first k-1 time levels by using a method recently developed for fractional evolution equations. An error bound of O(t_n^-kτ^k+t_n^-1h^2|h|) is established for the fully discrete finite element method for general L^2 initial data.