An unfitted finite-element method for elliptic and parabolic interface problems

A finite-element discretization, independent of the location of the interface, is proposed and analysed for linear elliptic and parabolic interface problems. We establish error estimates of optimal order in the H 1 norm and almost optimal order in the L-2-norm for elliptic interface problems. An extension to parabolic interface problems is also discussed and an optimal error estimate in the L-2 (0, T; H-1 (Omega))-norm and an almost optimal order estimate in the L-2(0, T; L-2(Omega))-norm are derived for the spatially discrete scheme. A fully discrete scheme based on the backward Euler method is analysed and an optimal order error estimate in the L-2(0, T; H-1(Omega))-norm is derived. The interfaces are assumed to be of arbitrary shape and smooth for our purpose.