Abstract
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; H1 (Ω))-norm and an almost optimal order estimate in the L 2 (0, T; L 2 (Ω))-norrn 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 I (Ω))-norm is derived. The interfaces are assumed to be of arbitrary shape and smooth for our purpose.
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