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We define a new finite element method for a steady state elliptic problem with discontinuous diffusion coefficients where the meshes are not aligned with the interface. We prove optimal error estimates in the \(L^2\) norm and \(H^1\) weighted semi-norm independent of the contrast between the coefficients. Numerical experiments validating our theoretical findings are provided.

A Finite Element Method for High-Contrast Interface Problems with Error Estimates Independent of Contrast