An unfitted interface penalty finite element method for elliptic interface problems

An unfitted interface penalty finite element method (UIPFEM) is proposed for the elliptic interface problems, in which Nitsche's method together with the ideas of merging elements and harmonic weighting fluxes are used. Both the convergence rate of the UIPFE solution and the condition number of the algebraic system are optimal and independent of the interface position. Furthermore, the error estimates do not depend on the ratio of the discontinuous coefficients. Numerical examples are also given to confirm the theoretical results.