This work focuses on the finite element discretization of boundary value problems whose solution features either a discontinuity or a discontinuous conormal derivative across an in- terface inside the computational domain. The interface is characterized via a level set function. The discontinuities are accounted for by using suitable extension operators whose numerical implementa- tion requires a very low computational effort. After carrying out the error analysis, numerical results to validate our approach are presented in one, two, and three dimensions.

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