Numerical Approximation of Internal Discontinuity Interface Problems

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 interface 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 implementation 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.