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-$$Q_1$$Q1 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 $$L^2$$L2-norms are proved to be better than $$O(h\sqrt{|\log h|})$$O(h|logh|) and $$O(h^2|\log h|)$$O(h2|logh|), respectively, where the $$|\log h|$$|logh| factors reflect jump discontinuity. Numerical results are reported to confirm our analysis.

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