A Nonconforming Immersed Finite Element Method for Elliptic Interface Problems

A new immersed finite element (IFE) method is developed for second-order elliptic problems with discontinuous diffusion coefficient. The IFE space is constructed based on the rotated- $$Q_1$$ nonconforming finite elements with the integral-value degrees of freedom. The standard nonconforming Galerkin method is employed in this IFE method without any stabilization term. Error estimates in energy and $$L^2$$ -norms are proved to be better than $$O(h\sqrt{|\log h|})$$ and $$O(h^2|\log h|)$$ , respectively, where the $$|\log h|$$ factors reflect jump discontinuity. Numerical results are reported to confirm our analysis.