Sensitive measurement and control equipment are protected from disturbing electromagnetic fields by thin shielding sheets. Alternatively to discretisation of the sheets, the electromagnetic fields are modeled only in the surrounding of the layer taking them into account with the so called Generalised Impedance Boundary Conditions.We study the shielding effect by means of the model problem of a diffusion equation with additional dissipation in the curved thin sheet. We use the asymptotic expansion techniques to derive a limit problem, when the thickness of the sheet ε tends to zero, as well as the models for contribution to the solution of higher order in ε. These problems are posed in limit area of vanishing ε with condition for the jump of the solution and it's normal derivative, which avoid to mesh the computational domain, even locally, at the scale of ε.We derive the problems for arbitrary order and show their existence and uniqueness. Numerical experiments for the problems up to second order show the asymptotic convergence of the solution of right order in mean of the thickness parameter ε.Copyright line will be provided by the publisher Outline of the problemThe diffusion-reaction equation in 2Dis a model problem for the magnetoquasistatic Eddy-current model with a thin conducting sheet [1], whereas c(x) is vanishing besides the thin sheet Ω C of constant thickness d. Domains with very thin sheets are hardly to mesh by todays grid generators. Thus, one would like to replace the sheet by an internal interface, where Generalised Impedance Boundary conditions (GIBCs)[2], [3] model the effect of the sheet. We will derive higher order GIBCs by asymptotic expansions [4] for smooth sheets and constant conductivity c(x). Even so we are looking for the solution for a sheet of a particular thickness d, we replace (1) by a family of problems (see Fig. 1), ordered by the thickness parameter εWe consider these equations for all ε < ε 0 , such that the support of f is outside the sheet Ω ε int . We choose in this model a conductivity scaled like 1 /ε. To solve for a particular thickness d, one select c 0 = c d, by what the problems (2) and (1) coincide for ε = d. Due to this scaling the limit solution for ε → 0 is non-trivial, meaning that neither the effect of the sheet disappear nor the sheet gets a perfect conductor. The external solution u ε ext (x) in the non-conducting subdomain Ω ε ext and the internal solution u ε int (x) in Ω ε int are related by Dirichlet and Neumann transmission conditions. Asymptotic expansionsExternal functions In the external domain Ω ε ext we are looking for an asymptotic of the solution with the formInternal functions We introduce local coordinates (t, s) in the sheet, where t is the tangential coordinate along the midline Γ m and s ∈ [−ε/2, ε/2] is the coordinate in thickness direction. Furthermore, let S = s/ε the stretched coordinate, the parameter domain of (t, S) is called Ω and the internal solution is U ε int (t, S) := u ε int (t, s). We are looking for an asymptotic of the soluti...

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