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 root vertical bar log h vertical bar) and O(h(2)vertical bar log h vertical bar), respectively, where the vertical bar log h vertical bar factors reflect jump discontinuity. Numerical results are reported to confirm our analysis.